1
IIT-JEE 2009 Paper 1 Offline
+3
-1

A disk of radius $${a \over 4}$$ having a uniformly distributed charge 6C is placed in the xy-plane with its centre at ($$-$$a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two points charges $$-$$7C and 3C are placed at (a/4, $$-$$a/4, 0) and ($$-$$3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces $$x=\pm a/2,y=\pm a/2,z=\pm a/2$$. The electric flux through this cubical surface is

A
$${{ - 2c} \over {{\varepsilon _0}}}$$
B
$${{2c} \over {{\varepsilon _0}}}$$
C
$${{10c} \over {{\varepsilon _0}}}$$
D
$${{12c} \over {{\varepsilon _0}}}$$
2
IIT-JEE 2009 Paper 1 Offline
+3
-1

Three concentric metallic spherical shells of radii $$R,2R,3R$$ are given charges $$Q_1,Q_2,Q_3$$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $$Q_1:Q_2:Q_3$$, is

A
1 : 2 : 3
B
1 : 3 : 5
C
1 : 4 : 9
D
1 : 8 : 18
3
IIT-JEE 2009 Paper 1 Offline
+3
-0

Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and $$\mu$$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

Column I Column II
(A) $$E=0$$ (P)
Charge are at the corners of a regular hexagon. M is at the centre of the hexagon. PQ is perpendicular to the plane of the hexagon.
(B) $$V\ne 0$$ (Q)
Charges are on a line perpendicular to PQ at equal intervals. M is the midpoint between the two innermost charges.
(C) $$B=0$$ (R)
Charges are placed on two coplanar insulating rings at equal intervals. M is the common centre of the rings. PQ is perpendicular to the plane of the rings.
(D) $$\mu \ne 0$$ (S)
Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. PQ is parallel to the longer sides.
(T)
Charges are placed on two coplanar, identical insulating rings are equal intervals. M is the midpoint between the centres of the rings. PQ is perpendicular to the line joining the centres and coplanar to the rings.

A
$$\mathrm{(A)\to(R),(S);(B)\to(R),(S);(C)\to(P),(Q),(T);(D)\to(T),(S)}$$
B
$$\mathrm{(A)\to(P),(R),(S);(B)\to(R),(S);(C)\to(P),(Q),(S);(D)\to(R),(S)}$$
C
$$\mathrm{(A)\to(P),(R),(S);(B)\to(R),(S);(C)\to(P),(Q),(T);(D)\to(R),(S)}$$
D
$$\mathrm{(A)\to(P),(Q),(S);(B)\to(R),(S);(C)\to(P),(Q),(T);(D)\to(R),(S)}$$
4
IIT-JEE 2008 Paper 2 Offline
+3
-1

Consider a system of three charges $${q \over 3},{q \over 3}$$ and $$- {{2q} \over 3}$$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60$$^\circ$$

A
The electric field at point O is $${q \over {8\pi {\varepsilon _0}{R^2}}}$$ directed along the negative x-axis
B
The potential energy of the system is zero
C
The magnitude of the force between the charges at C and B is $${{{q^2}} \over {54\pi {\varepsilon _0}{R^2}}}$$
D
The potential at point O is $${q \over {12\pi {\varepsilon _0}R}}$$
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