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The potential of the electric field produced by a point charge at any point (x, y, z) is given by $V = 3x^2 + 5$, where x, y, z are in metres and V is in volts. The intensity of the electric field at (–2, 1, 0) is
1. +17 Vm^–1 
2. –17 Vm^–1
3. +12 Vm^–1 
4. –12 Vm^–1

Eight charged water drops each with a radius of 1mm and a charge of 10^–10 C merge into single drop. Potential of the big drop will be
1. 3600 V 
2. 900 V
3. 300 V 
4. 150 V

Three concentric spherical shells have radii a, b and
c (a < b < c) and have surface charge densities $\mathrm{\sigma }$, –$\mathrm{\sigma }$
and $\mathrm{\sigma }$ respectively. If V_A, V_B and V_C denote the
potentials of the three shells, then for c = a + b, we
have
1. VC = VB $\ne$ VA 
2. VC $\ne$ VB $\ne$ VA
3. VC = VB = VA 
4. VC = VA $\ne$ VB

Charges +q and –q are placed at points A and B respectively which are at a distance 2L apart, C is the mid-point between A and B. The work done in moving a charge +Q along the semicircle CRD is

1. $\frac{\mathrm{qQ}}{2{\mathrm{\pi \epsilon }}_0\mathrm{L}}$
2. $\frac{\mathrm{qQ}}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$
3. $\frac{-\mathrm{qQ}}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$
4. $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

An air capacitor C, is connected to a battery of emf V. It acquires a charge Q and energy E. The capacitor is then disconnected from the battery and a dielectric slab is introduced between the plates. Which of the following is true?
1. V & Q decrease but E & C increase
2. V remains unchanged but Q, E and C
increase
3. Q remains unchanged, C increases, V and
E decreases
4. Q & C increase but V & E decrease

Two condensers, one of capacity C and the other of capacity $\frac{\mathrm{C}}{2}$ , are connected to a V volt battery, as shown

1. $2{\mathrm{CV}}^2$
2. $\frac{1}{4}C{V}^2$
3. $\frac{3}{4}C{V}^2$
4. $\frac{1}{2}C{V}^2$

The energy required to charge a parallel plate
condenser of plate separation d and plate area of
cross-section A such that the uniform electric field
between the plates is E, is 
1. ${\mathrm{\epsilon }}_0{\mathrm{E}}^2/\mathrm{Ad}$
2. ${\mathrm{\epsilon }}_0{\mathrm{E}}^2\mathrm{d}$
3. $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$
4. $\frac{1}{2}{\epsilon }_0{E}^2\mathit{/}Ad$

In the figure below, the capacitance of each capacitor
is 3$\mathrm{\mu }$F. The effective capacitance between A and B is

1. $\frac{3}{4} \mu F$
2. $3 \mathrm{\mu F}$
3. $6 \mathrm{\mu F}$
4. $5 \mathrm{\mu F}$

The equivalent capacity between the points X and Y
in the circuit with C = 1 $\mathrm{\mu }$F is

1. $2 \mathrm{\mu F}$
2. $3 \mathrm{\mu F}$
3. $1 \mathrm{\mu F}$
4. $0.5 \mathrm{\mu F}$

A parallel plate capacitor with air as dielectric is
charged to a potential ‘V’ using a battery. Removing
the battery, the charged capacitor is then connectged
across an identical uncharged parallel plate capacitor
filled with wax of dielectric constant ‘k’. The common
potential of both the capacitors is
1. V volts
2. kV volts
3. (k+1) V volts
4. $\frac{\mathrm{V}}{\mathrm{k}+1} volts$

What is the potential difference across 3 $\mathrm{\mu }$F capacitor
in the circuit shown in the figure?

1. 6V 
2. 2V
3. 4V 
4. 16V

A parallel plate capacitor with air as the dielectric has
capacitance C. A slab of dielectric constant K and
having the same thickness as the separation between
the plates is introduced so as to fill one-fourth of the
capacitor as shown in the figure. The new capacitance
will be

1. $\left(\mathrm{K}+3\right)\frac{C}{4}$
2. $\left(\mathrm{K}+2\right)\frac{C}{4}$
3. $\left(\mathrm{K}+1\right)\frac{C}{4}$
4. $\frac{\mathrm{KC}}{4}$

In the given circuit diagram, initially battery was
connected. Find the work done by battery if capacitor
is completely filled with a dielectric of dielectric
constant k = 3.

1. $\frac{1}{2}C{V}^2$
2. ${\mathrm{CV}}^2$
3. $2{\mathrm{CV}}^2$
4. $\frac{3}{2}C{V}^2$

The electric potential V at any point x, y, z (all in
metres) in space is given by V = 4x² volts. The electric
field (in V/m) at the point (1 m, 0, 2 m)
1. $-8 \hat{\mathrm{i}}$
2. $8 \hat{\mathrm{i}}$
3. $-16 \hat{\mathrm{i}}$
4. $8\sqrt{5} \hat{\mathrm{i}}$

In a parallel-plate capacitor of capacitance C, a metal
sheet is inserted between the plates, parallel to them.
The thickness of the sheet is half of the separation
between the plate. The capacitance now becomes
1. 4C 
2. 2C
3. C/2 
4. C/4

Capacitance of a capacitor becomes $\frac{4}{3}$ times its
original value if a dielectric slab of thickness t = d/2 is
inserted between the plates (d = separation between
the plates). The dielectric constant of the slab is
1. 2 
2. 4
3. 6 
4. 8

In the figure shown, conducting shells A and B have
charges Q and 2Q distributed uniformly over A and
B .Value of V_A – V_B is

1. $\frac{\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$
2. $\frac{\mathrm{Q}}{8{\mathrm{\pi \epsilon }}_0\mathrm{R}}$
3. $\frac{3\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$
4. $\frac{3\mathrm{Q}}{8{\mathrm{\pi \epsilon }}_0\mathrm{R}}$

Three point charges q, –2q and –2q are placed at the
vertices of an equilateral triangle of side a. The work
done by some external force to slowly increase their
separation to 2a will be
1. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2q^2}{a}$
2. $\frac{q^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{a}}$
3. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathit{3}{q}^2}{3R}$
4. Zero

Two capacitors of capacitance 3 $\mathrm{\mu }$ F and 6 $\mathrm{\mu }$ F are
charged to a potential of 12 V each. They are now
connected to each other, with the positive plate of
one to the negative plate of the other. Then
1.  the potential difference across 3 $\mathrm{\mu }$ F is zero
2. the potential difference across 3 $\mathrm{\mu }$ F is 4 V
3. the charge on 3 $\mathrm{\mu }$ F is zero
4. the charge on 3 $\mathrm{\mu }$ F is 10 $\mathrm{\mu }$ C

Figure shows some of the electric field lines corresponding to an electric field. The figure suggests that (E = electric field, V = potential)

1. V_A = V_B 
2. E_A = E_B
3. V_A V_B 
4. V_A < V_B