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1

AIEEE 2006

MCQ (Single Correct Answer)
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 $$2$$ is at a higher potential). The plates are separated by $$d=0.1$$ $$m$$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $$1.$$ What is its speed when it hits plate $$2$$?
$$\left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)$$
A
$$2.65 \times {10^6}\,m/s$$
B
$$7.02 \times {10^{12}}\,m/s$$
C
$$1.87 \times {10^6}\,m/s$$
D
$$32 \times {10^{ - 19}}\,m/s$$

Explanation

$$eV = {1 \over 2}m{v^2}$$

$$ \Rightarrow v = \sqrt {{{2ev} \over m}} = \sqrt {{{2 \times 1.6 \times {{10}^{ - 19}} \times 20} \over {9.31 \times {{10}^{ - 31}}}}} $$

$$ = 2.65 \times {10^6}\,m/s$$
2

AIEEE 2006

MCQ (Single Correct Answer)
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. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $$A$$ and $$B$$ is
A
$$4:1$$
B
$$1:2$$
C
$$2:1$$
D
$$1:4$$

Explanation



After connection, $${V_1} = {V_2}$$

$$ \Rightarrow K{{{Q_1}} \over {{r_1}}} = K{{{Q_2}} \over {{r^2}}}$$

$$ \Rightarrow {{Q{}_1} \over {{r_1}}} = {{{Q_2}} \over {{r_2}}}$$

The ratio of electric fields

$${{{E_1}} \over {{E_2}}} = {{K{{{Q_1}} \over {r_1^2}}} \over {K{{{Q_2}} \over {r_2^2}}}} = {{{Q_1}} \over {r_1^2}} \times {{r_2^2} \over {{Q_2}}}$$

$$ \Rightarrow {{{E_1}} \over {{E_2}}} = {{{r_1} \times r_2^2} \over {r_1^2 \times {r_2}}} \Rightarrow {{{E_1}} \over {{E_2}}} = {{{r_2}} \over {{r_1}}} = {2 \over 1}$$

Since the distance between the spheres is large as compared to their diameters, the induced effects may be ignored.
3

AIEEE 2006

MCQ (Single Correct Answer)
An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience
A
a translation force only in the direction of the field
B
a translation force only in a direction normal to the direction of the field
C
a torque as well as a translational force
D
a torque only

Explanation



The electric field will be different at the location of the two charges. Therefore the two forces will be unequal. This will result in a force as well as torque.
4

AIEEE 2005

MCQ (Single Correct Answer)
A fully charged capacitor has a capacitance $$'C'$$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $$'s'$$ and mass $$'m'.$$ If the temperature of the block is raised by $$'\Delta T',$$ the potential difference $$'v'$$ across the capacitance is
A
$${{mCAT} \over s}$$
B
$$\sqrt {{{2mCAT} \over s}} $$
C
$$\sqrt {{{2msAT} \over C}} $$
D
$${{ms\Delta T} \over C}$$

Explanation

Applying conservation of energy,

$${1 \over 2}C{V^2} = m.s\Delta T;\,\,\,$$

$$V = \sqrt {{{2m.s.\Delta T} \over C}} $$

Questions Asked from Electrostatics

On those following papers in MCQ (Single Correct Answer)
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