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1.

A hollow conducting sphere is placed in an electric field produced by a point charge placed at \(P\) as shown in the figure. Let\(​​V_A ~,V_B~,V_C\) be the potentials at points \(A\), \(B\) and \(C\) respectively. Then:
     
1. \(V_A<V_B<V_C\)
2. \(V_A>V_B>V_C\)
3. \(V_C>V_B=V_A\)
4. \(V_A=V_B=V_C\)

2.

The capacitance of a parallel plate capacitor is C. If a dielectric slab of thickness equal to one-fourth of the plate separation and dielectric constant K is inserted between the plates, then new capacitance become
1. $\frac{KC}{2\left(K+1\right)}$
2. $\frac{2KC}{K+1}$
3. $\frac{5KC}{4K+1}$
4. $\frac{4KC}{3K+1}$

3. When a proton at rest is accelerated by a potential difference \(V\), its speed is found to be \(v\). The speed of an \(\alpha\text{-particle}\) when accelerated by the same potential difference from rest will be: 

1.	\(v\)	2.	\(v \over \sqrt{2}\)
3.	\(v \sqrt{2}\)	4.	\(2v\)

4.

In the circuit shown in figure, energy stored in \(6~\mu\text{F}\) capacitor will be:
   

1.	\(48 \times10^{-6}~\text{J}\)	2.	\(32 \times10^{-6}~\text{J}\)
3.	\(96 \times10^{-6}~\text{J}\)	4.	\(24 \times10^{-6}~\text{J}\)

5.

The figure shows some of the equipotential surfaces. Magnitude and direction of the electric field is given by
           
1. 200 V/m, making an angle ${120}^0$ with the x-axis
2. 100 V/m, pointing towards the negative x-axis
3. 200 V/m, making an angle $-{60}^0$ with the x-axis
4. 100 V/m, making an angle ${30}^0$ with the x-axis

6.

A and B are two concentric metallic shells. If A is positively charged and B is earthed, then electric
                                             
1.  Field at common centre is non-zero
2.  Field outside B is nonzero
3.  Potential outside B is positive
4.  Potential at common centre is positive

7.

Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle θ with the axis of the dipole, then the potential at P is given by (r >> 2a) (Where p = 2qa) 
(1) $V=\frac{p\cos \theta }{4\pi {\epsilon }_0{r}^2}$
(2) $V=\frac{p\cos \theta }{4\pi {\epsilon }_{0}r}$
(3) $V=\frac{p\sin \theta }{4\pi {\epsilon }_{0}r}$
(4) $V=\frac{p\cos \theta }{2\pi {\epsilon }_0{r}^2}$ 

8.

A charge \(+q\) is fixed at each of the points $x=x_0,$ $x=3x_0,$ $x=5x_0$ ..... infinite, on the \(x\)-axis, and a charge \(-q\) is fixed at each of the points $x=2x_0,$ $x=4x_0,x=6x_0$,..... infinite. Here \(x_0\) is a positive constant. Take the electric potential at a point due to a charge \(Q\) at a distance \(r\) from it to be \(\frac{Q}{4\pi \varepsilon_0 r}\). Then, the potential at the origin due to the above system of charges is:
1. \(0\)
2. \(\frac{q}{8 \pi \varepsilon_{0} x_{0} \mathrm{ln} 2}\)
3. \(\infty\)
4. \(\frac{q \mathrm{ln} 2}{4 \pi \varepsilon_{0} x_{0}}\)

9.

A conductor with a positive charge:

1.	is always at +ve potential.
2.	is always at zero potential.
3.	is always at negative potential.
4.	may be at +ve, zero or –ve potential.

10.

Two spheres A and B of radius 4 cm and 6 cm are given charges of 80 μc and 40μc respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is -
(1) 20μc from A to B
(2) 16μc from A to B
(3) 32μc from B to A
(4) 32μc from A to B

11. A cube of a metal is given a positive charge \(Q.\) For the above system, which of the following statements is true?

1.	The electric potential at the surface of the cube is zero.
2.	The electric potential within the cube is zero.
3.	The electric field is normal to the surface of the cube.
4.	The electric field varies within the cube.

12.

Two charges \(q_1\) and \(q_2\) are placed \(30~\text{cm}\) apart, as shown in the figure. A third charge \(q_3\) is moved along the arc of a circle of radius \(40~\text{cm}\) from \(C\) to \(D.\) The change in the potential energy of the system is \(\dfrac{q_{3}}{4 \pi \varepsilon_{0}} k,\) where \(k\) is:

1.	\(8q_2\)	2.	\(8q_1\)
3	\(6q_2\)	4.	\(6q_1\)

13.

If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).

14.

A light bulb, a capacitor and a battery are connected together as shown below with the switch S initially open. When the switch S is closed, which one of the following is true?
      
1. The bulb will light up for an instant when
    the capacitor starts charging.
2. The bulb will light up when
    the capacitor is fully charged.
3. The bulb will not light up at all.
4. The bulb will light up and go off at regular intervals.

15.

A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V₀. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is 
(1) $\frac{3{\epsilon }_{0}A{V}_0^2}{d}$
(2) $\frac{{\epsilon }_{0}A{V}_0^2}{2d}$
(3) $\frac{{\epsilon }_{0}A{V}_0^2}{3d}$
(4) $\frac{{\epsilon }_{0}A{V}_0^2}{d}$