JEE Main
Physics
Electrostatics
Previous Years Questions

## Numerical

A cubical volume is bounded by the surfaces $$\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}$$. The electric field in the r...
Two equal positive point charges are separated by a distance $$2 a$$. The distance of a point from the centre of the line joining two charges on the e...
Expression for an electric field is given by $$\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}$$. The electric flux throu...
As shown in figure, a cuboid lies in a region with electric field $E=2 x^{2} \hat{i}-4 y \hat{j}+6 \hat{k} \mathrm{~N} / \mathrm{C}$. The magnitude of...
For a charged spherical ball, electrostatic potential inside the ball varies with $$r$$ as $$\mathrm{V}=2ar^2+b$$. Here, $$a$$ and $$b$$ are constant ...
A point charge $$q_1=4q_0$$ is placed at origin. Another point charge $$q_2=-q_0$$ is placed at $$x=12$$ cm. Charge of proton is $$q_0$$. The proton i...
A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically bet...
A stream of a positively charged particles having $${q \over m} = 2 \times {10^{11}}{C \over {kg}}$$ and velocity $${\overrightarrow v _0} = 3 \times ... Two electric dipoles of dipole moments$$1.2 \times 10^{-30} \,\mathrm{Cm}$$and$$2.4 \times 10^{-30} \,\mathrm{Cm}$$are placed in two different uni... A long cylindrical volume contains a uniformly distributed charge of density$$\rho \,\mathrm{Cm}^{-3}$$. The electric field inside the cylindrical vo... Three point charges of magnitude$$5 \mu \mathrm{C}, 0.16 \mu \mathrm{C}$$and$$0.3 \mu \mathrm{C}$$are located at the vertices$$A, B, C$$of a rig... The volume charge density of a sphere of radius$$6 \mathrm{~m}$$is$$2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}$$. The number of lines of force per unit ... Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger d... 27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V. A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge ... The total charge enclosed in an incremental volume of 2$$\times$$10$$-$$9 m3 located at the origin is ___________ nC, if electric flux density of it... A body having specific charge 8$$\mu$$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts mo... An infinite number of point charges, each carrying 1$$\mu$$C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............The total f... The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric field intensity produced by th... The electric field in a region is given by$$\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j$$with$${E_0} = 4.0 \times ...
27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger d...
The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is $${x \over {10}}\sqrt {{{{\mu _0}c} \over \pi }} {V... Two identical conducting spheres with negligible volume have 2.1 nC and$$-$$0.1 nC charges, respectively. They are brought into contact and then sepa... Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of ... The electric field in a region is given by$$\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}$... 512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ______... A point charge of +12$$\mu$$C is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the ele... An electric field $$\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j$$ N/C passes through the box shown in figure. The flux of... ## MCQ (Single Correct Answer) Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different re... Considering a group of positive charges, which of the following statements is correct ? Which of the following correctly represents the variation of electric potential $$(\mathrm{V})$$ of a charged spherical conductor of radius $$(\mathrm... A point source of 100 \mathrm{~W} emits light with 5 \% efficiency. At a distance of 5 \mathrm{~m} from the source, the intensity produced by th... As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner radius a and outer radius b. The electri... Electric field in a certain region is given by$$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\r... Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2 \mathrm{R}$$ are charged such that both have same charge density $$\sigma$$. The s... A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axi... In a cuboid of dimension $$2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$$, a charge $$q$$ is placed at the center of the surface '$$\mathrm{S}... A point charge of 10$$\mu$$C is placed at the origin. At what location on the X-axis should a point charge of 40$$\mu$$C be placed so that the net e... The electric potential at the centre of two concentric half rings of radii R$$_1$$and R$$_2$$, having same linear charge density$$\lambda$$is : ... If two charges q$$_1$$and q$$_2$$are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distan... Two identical metallic spheres$$\mathrm{A}$$and$$\mathrm{B}$$when placed at certain distance in air repel each other with a force of$$\mathrm{F}$...
A spherically symmetric charge distribution is considered with charge density varying as $$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}... Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric fiel... A uniform electric field$$\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}$$is created between two parallel plates of length$$1 \m...
A charge of $$4 \,\mu \mathrm{C}$$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided c...
Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$q_{0}$$ with mass 'm' is place...
An electron (mass $$\mathrm{m}$$) with an initial velocity $$\vec{v}=v_{0} i\left(v_{0}>0\right)$$ is moving in an electric field $$\vec{E}=-E_{0} \ha... Two uniformly charged spherical conductors$$A$$and$$B$$of radii$$5 \mathrm{~mm}$$and$$10 \mathrm{~mm}$$are separated by a distance of$$2 \mat...
Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisect...
If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1, 0, 3) m will be :...
A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $$\times$$ 105 NC$$-$$1. If the charge ...
Two point charges A and B of magnitude +8 $$\times$$ 10$$-$$6 C and $$-$$8 $$\times$$ 10$$-$$6 C respectively are placed at a distance d apart. The el...
Given below are two statements : Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the char...
The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) ...
If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be : ...
Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an eq...
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $$\mu$$C are combined to form a bigger drop. The ratio of surface de...
Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Non-polar materials do not have any...
Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10$$-$$7C are placed on a horizontal table with a separation of L b...
A long cylindrical volume contains a uniformly distributed charge of density $$\rho$$. The radius of cylindrical volume is R. A charge particle (q) re...
A vertical electric field of magnitude 4.9 $$\times$$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the d...
A cube is placed inside an electric field, $$\overrightarrow E = 150{y^2}\widehat j$$. The side of the cube is 0.5 m and is placed in the field as sh...
Choose the incorrect statement :(1) The electric lines of force entering into a Gaussian surface provide negative flux.(2) A charge 'q' is placed at t...
Two particles A and B having charges 20$$\mu$$C and $$-$$5$$\mu$$C respectively are held fixed with a separation of 5 cm. At what position a third cha...
Figure shows a rod AB, which is bent in a 120$$^\circ$$ circular arc of radius R. A charge ($$-$$Q) is uniformly distributed over rod AB. What is the ...
A uniformly charged disc of radius R having surface charge density $$\sigma$$ is placed in the xy plane with its center at the origin. Find the electr...
The two thin coaxial rings, each of radius 'a' and having charges +Q and $$-$$Q respectively are separated by a distance of 's'. The potential differe...
A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in th...
What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?...
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium sepa...
Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the fi...
An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $$\times$$ 10$$-$$6 C/m. Line charge is placed on z-...
A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point the direction of current density is at an ang...
A certain charge Q is divided into two parts q and (Q $$-$$ q). How should the charges Q and q be divided so that q and (Q $$-$$ q) placed at a certai...
An oil drop of radius 2 mm with a density 3g cm$$-$$3 is held stationary under a constant electric field 3.55 $$\times$$ 105 V m$$-$$1 in the Millikan...
Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along ...
Given below are two statements: Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through th...
An inclined plane making an angle of 30$$^\circ$$ with the horizontal is placed in a uniform horizontal electric field $$200{N \over C}$$ as shown in ...
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q...
A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E$$ through the shaded area is :...
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) per...
A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the cen...
Two identical electric point dipoles have dipole moments $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$ and ...
Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one...
Charges Q1 and Q2 are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the ...
Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, ...
A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached f...
A particle of charge q and mass m is subjected to an electric field E = E0 (1 – $$a$$x2) in the x-direction, where $$a$$ and E0 are constants. Initi...
Two charged thin infinite plane sheets of uniform surface charge density $${\sigma _ + }$$ and $${\sigma _ - }$$, where |$${\sigma _ + }$$| > |$${\... A two point charges 4q and -q are fixed on the x-axis at x =$$ - {d \over 2}$$and x =$${d \over 2}$$respectively. If a third point charge 'q' is t... Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric sphe... Two isolated conducting spheres S1 and S2 of radius$${2 \over 3}R$$and$${1 \over 3}R$$have 12$$\mu $$C and –3$$\mu $$C charges, respectively, an... A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two sh... A charged particle (mass m and charge q) moves along X-axis with velocity V0. When it passes through the origin it enters a region having uniform elec... Consider a sphere of radius R which carries a uniform charge density$$\rho $$. If a sphere of radius$${{R \over 2}}$$is carved out of it, as shown,... An electric dipole of moment$$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $$C.m is at the or... A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its... Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are ... In finding the electric field using Gauss Law the formula$$\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|...
Three charged particle A, B and C with charges –4q, 2q and –2q are present on the circumference of a circle of radius d. the charged particles A, C an...
Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30o. The electric field in the r...
Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho$$(r) = kr, where r is the distance from the cen...
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $$\overr... A point dipole$$\overrightarrow p = - {p_0}\widehat x$$is kept at the origin. The potential and electric field due to this dipole on the y-axis at... In free space, a particle A of charge 1$$\mu $$C is held fixed at a point P. Another particle B of the same charge and mass 4$$\mu $$g is kept at a di... A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along th... Four point charges –q, +q, +q and –q are placed on y-axis at y = –2d, y = –d, y = +d and y = +2d, respectively. The magnitude of the electric field E ... A system of three charges are placed as shown in the figure : If D >> d, the potential energy of the system is best given by : ... A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as... The electric field in a region is given by$$\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge $$, where E is in NC–1 and x ... The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equili... A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between th... Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure : ... Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the config... Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpen... A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal... Two electric dipoles, A, B with respective dipole moments$${\overrightarrow d _A} = - 4qai$$and$${\overrightarrow d _B} = - 2qai$$are placed on ... Two point charges q1$$\left( {\sqrt {10} \mu C} \right)$$and q2($$-$$25$$\mu $$C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The... Charge is distributed within a sphere of radius R with a volume charge density$$\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$$w... Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, pla... For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h i... Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force betwe... Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities$$ + \sigma $$,$$ - \sigma $$... A solid ball of radius R has a charge density$$\rho $$given by$$\rho $$=$$\rho $$o (1$$-{\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\...
A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-direction about its equilibrium ...
A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure. The electric flux through the ...
Four closed surfaces and corresponding charge distributions are shown below. Let the respective electric fluxes through the surfaces be $${\Phi _1},... There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at$$P,$$in the region, is found to var... The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4$$\mu $$C charge, its radius will be : [ Take : ... An electric dipole has a fixed dipole moment$$\overrightarrow p $$, which makes angle$$\theta$$with respect to x-axis. When subjected to an electri... Within a spherical charge distribution of charge density$$\rho $$(r), N equipotential surfaces of potential V0, V0 +$$\Delta $$V, V0 + 2$$\Delta $$V... The potential (in volts) of a charge distribution is given by. V(z) = 30$$-$$5x2 for$$\left| z \right| \le $$1 m. V(z) = 35$$-$$10$$\left|...
The region between two concentric spheres of radii $$'a'$$ and $$'b',$$ respectively (see figure), have volume charge density $$\rho = {A \over r},$$...
A long cylindrical shell carries positives surfaces change $$\sigma$$ in the upper half and negative surface charge - $$\sigma$$ in the lower half. ...
Assume that an electric field $$\overrightarrow E = 30{x^2}\widehat i$$ exists in space. Then the potential difference $${V_A} - {V_O},$$ where $${V_... Two charges, each equals to$$q,$$are kept at$$x=-a$$and$$x=a$$on the$$x$$-axis. A particle of mass$$m$$and charge$${q_0} = {q \over 2}$$is ... A charge$$Q$$is uniformly distributed over a long rod$$AB$$of length$$L$$as shown in the figure. The electric potential at the point$$O$$lying... In a uniformly charged sphere of total charge$$Q$$and radius$$R,$$the electric field$$E$$is plotted as function of distance from the center. The... This question has statement-$$1$$and statement-$$2.$$Of the four choices given after the statements, choose the one that best describe the two sta... Two identical charged spheres suspended from a common point by two massless strings of length$$l$$are initially a distance$$d\left( {d < < 1...
The electrostatic potential inside a charged spherical ball is given by $$\phi = a{r^2} + b$$ where $$r$$ is the distance from the center and $$a,b$$...
Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \o... A thin semi-circular ring of radius$$r$$has a positive charges$$q$$distributed uniformly over it. The net field$$\overrightarrow E $$at the cent... Let$$P\left( r \right) = {Q \over {\pi {R^4}}}r$$be the change density distribution for a solid sphere of radius$$R$$and total charge$$Q$$. For a... (This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statem... A charge$$Q$$is placed at each of the opposite corners of a square. A charge$$q$$is placed at each of the other two corners. If the net electrica... Two points$$P$$and$$Q$$are maintained at the potentials of$$10V$$and$$-4V$$, respectively. The work done in moving$$100$$electrons ... A thin spherical shell of radius$$R$$has charge$$Q$$spread uniformly over its surface. Which of the following graphs most closely represents the e... An electric charge$${10^{ - 3}}\,\,\mu \,C$$is placed at the origin$$(0,0)$$of$$X-Y$$co-ordinate system. Two points$$A$$and$$B$$are situated... The potential at a point$$x$$(measured in$$\mu \,m$$) due to some charges situated on the$$x$$-axis is given by$$V\left( x \right) = 20/\left( {{...
Charges are placed on the vertices of a square as shown. Let $$\overrightarrow E$$ be the electric field and $$V$$ the potential at the center. If th...
A parallel plate condenser with a dielectric of dielectric constant $$K$$ between the plates has a capacity $$C$$ and is charged to a potential $$V$$ ...
An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience
Two spherical conductors $$A$$ and $$B$$ of radii $$1$$ $$mm$$ and $$2$$ $$mm$$ are separated by a distance of $$5$$ $$cm$$ and are uniformly charged....
Two insulating plates are both uniformly charged in such a way that the potential difference between them is $${V_2} - {V_1} = 20\,V.$$ (i.e., plate $... Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respectively. The location of a point on the $$x$$ axis at which the net elec... Two thin wire rings each having a radius $$R$$ are placed at a distance $$d$$ apart with their axes coinciding. The charges on the two rings are $$+q... A charged ball$$B$$hangs from a silk thread$$S,$$which makes angle$$\theta $$with a large charged conducting sheet$$P,$$as shown in the figure... Two spherical conductors$$B$$and$$C$$having equal radii and carrying equal charges on them repel each other with a force$$F$$when kept apart at ... A charge particle$$'q'$$is shot towards another charged particle$$'Q'$$which is fixed, with a speed$$'v'$$. It approaches$$'Q'$$upto a closest ... Four charges equal to -$$Q$$are placed at the four corners of a square and a charge$$q$$is at its center. If the system is in equilibrium the valu... A charged oil drop is suspended in a uniform field of$$3 \times {10^4}v/m$$so that it neither falls nor rises. The charge on the drop will be ... If the electric flux entering and leaving an enclosed surface respectively is$${\phi _1}$$and$${\phi _2},$$the electric charge inside the surface ... A thin spherical conducting shell of radius$$R$$has a charge$$q.$$Another charge$$Q$$is placed at the center of the shell. The electrostatic pot... The work done in placing a charge of$$8 \times {10^{ - 18}}$$coulomb on a condenser of capacity$$100$$micro-farad is Three charges$$ - {q_1}, + {q_2}$$and$$ - {q_3}$$are placed as shown in the figure. The$$x$$-component of the force on$$ - {q_1}$$is proportion... On moving a charge of$$20$$coulomb by$$2cm,2J$$of work is done, then the potential differences between the points is A charged particle$$q$$is placed at the centre$$O$$of cube of length$$L(ABCDEFGH).$$Another same charge$$q$$is placed at a distance$$L$$from... If a charge$$q$$is placed at the center of the line joining two equal charges$$Q$$such that the system is in equilibrium then the value of$$q$$i... ## MCQ (More than One Correct Answer) A uniformly charged solid sphere of radius$$R$$has potential$${V_0}$$(measured with respect to$$\infty$\$) on its surface. For this sphere the eq...
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