Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by ρ(r) = kr, where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, ‘a’ from the centre. If A and B do not experience any force, then:

\({\rm{a}} = \frac{{3{\rm{R}}}}{{{2^{1/4}}}}\)

\({\rm{a}} = \frac{{\rm{R}}}{{\sqrt 3 }}\)

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 at a point on the x-axis at x = D, with D >> d, will behave as:

\(E \propto \frac{1}{{{D^2}}}\)

\(E \propto \frac{1}{{{D^3}}}\)

\(E \propto \frac{1}{{{D^4}}}\)

\(E \propto \frac{1}{{{D^2}}}\)

\(\left( {ql} \right)\frac{{\hat i + \hat j}}{{\sqrt 2 }}\)

\(\sqrt 3 ql\frac{{\hat j - \hat i}}{{\sqrt 2 }}\)

\(\left( {ql} \right)\frac{{\hat i + \hat j}}{{\sqrt 2 }}\)

\(\frac{{{\rm{K\epsilon_0}}{{\rm{a}}^2}}}{{\rm{d}}}{\rm{ln\;K}}\)

\(\frac{{{\rm{K}}{\epsilon _0}{{\rm{a}}^2}}}{{2{\rm{d}}\left( {{\rm{K}} + 1} \right)}}\)

\(\frac{{{\rm{K}}{\epsilon _0}{{\rm{a}}^2}}}{{{\rm{d}}\left( {{\rm{K}} - 1} \right)}}{\rm{ln\;K}}\)

\(\frac{{{\rm{K\epsilon_0}}{{\rm{a}}^2}}}{{\rm{d}}}{\rm{ln\;K}}\)

\(\frac{1}{2}\frac{{{\rm{K\epsilon_0}}{{\rm{a}}^2}}}{{\rm{d}}}\)

1.	Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by ρ(r) = kr, where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, ‘a’ from the centre. If A and B do not experience any force, then:
A.	a = 8-1/4R
B.	\({\rm{a}} = \frac{{3{\rm{R}}}}{{{2^{1/4}}}}\)
C.	a = 2-1/4R
D.	\({\rm{a}} = \frac{{\rm{R}}}{{\sqrt 3 }}\)
Answer» B. \({\rm{a}} = \frac{{3{\rm{R}}}}{{{2^{1/4}}}}\)

2.	In the above circuit, \(C = \sqrt {\frac{3}{2}} \;\mu F,{R_2} = 20\Omega ,\;L = \frac{{\sqrt 3 }}{{10}}H\) and R1 = 10 Ω Current in L – R1 path is I1 and in C - R2 path is I2. The voltage of AC source is given by \(V = 200\sqrt 2 \;sin\left( {100t} \right)\) difference between I1 and I2 is
A.	30°
B.	60°
C.	150°
D.	90°
Answer» D. 90°

3.	A positive charge +q is placed at the centre of a hollow metallic sphere of inner radius a and outer radius b. the electric field at a distance r from the centre is denoted by E. In this regards, which one of the following statement is correct?
A.	E = 0 for a < r < b
B.	E = 0 for r < a
C.	E = q / 4πϵ0r for a < r < b>
D.	E = q / 4πϵ0r for r < a
Answer» B. E = 0 for r < a

4.	If a free electron moves through a potential difference of 1 kV, then the energy gained by the electron is given by
A.	1.6 × 10-19 J
B.	1.6 × 10-16 J
C.	1 × 10-19 J
D.	1 × 10-16 J
Answer» C. 1 × 10-19 J

5.	A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is \(\left( {{\rm{Take,\;}}{{\rm{\varepsilon }}_0} = 8.85 \times {{10}^{ - 12}}\frac{{{{\rm{C}}^2}}}{{{\rm{N}} - {{\rm{m}}^2}}}} \right)\)
A.	9.85 × 10-10 C
B.	8.85 × 10-10 C
C.	7.85 × 10-10 C
D.	6.85 × 10-10 C
Answer» C. 7.85 × 10-10 C

6.	A parallel plate capacitor with air between the plates, has a capacitance of 2 pF. The plate separation is doubled and a dielectric slab is inserted so that it completely fills the space between the plates. The capacitance of the capacitor becomes 4 pF. The dielectric constant of the slab is:
A.	0.5
B.	2
C.	4
D.	8
Answer» D. 8

7.	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 at a point on the x-axis at x = D, with D >> d, will behave as:
A.	\(E \propto \frac{1}{{{D^3}}}\)
B.	\(E \propto \frac{1}{D}\)
C.	\(E \propto \frac{1}{{{D^4}}}\)
D.	\(E \propto \frac{1}{{{D^2}}}\)
Answer» D. \(E \propto \frac{1}{{{D^2}}}\)

8.	Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle as shown in the figure.
A.	\(\sqrt 3 ql\frac{{\hat j - \hat i}}{{\sqrt 2 }}\)
B.	\(2ql\hat j\)
C.	\(- \sqrt 3 ql\hat j\)
D.	\(\left( {ql} \right)\frac{{\hat i + \hat j}}{{\sqrt 2 }}\)
Answer» D. \(\left( {ql} \right)\frac{{\hat i + \hat j}}{{\sqrt 2 }}\)

9.	A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d << a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is:
A.	\(\frac{{{\rm{K}}{\epsilon _0}{{\rm{a}}^2}}}{{2{\rm{d}}\left( {{\rm{K}} + 1} \right)}}\)
B.	\(\frac{{{\rm{K}}{\epsilon _0}{{\rm{a}}^2}}}{{{\rm{d}}\left( {{\rm{K}} - 1} \right)}}{\rm{ln\;K}}\)
C.	\(\frac{{{\rm{K\epsilon_0}}{{\rm{a}}^2}}}{{\rm{d}}}{\rm{ln\;K}}\)
D.	\(\frac{1}{2}\frac{{{\rm{K\epsilon_0}}{{\rm{a}}^2}}}{{\rm{d}}}\)
Answer» C. \(\frac{{{\rm{K\epsilon_0}}{{\rm{a}}^2}}}{{\rm{d}}}{\rm{ln\;K}}\)