1
WB JEE 2021
+1
-0.25
A metal sphere of radius R carrying charge q is surrounded by a thick concentric metal shell of inner and outer radii a and b, respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surface of the shell is grounded will be
A
$${q \over {4\pi {\varepsilon _0}}}\left( {{1 \over a} - {1 \over b}} \right)$$
B
$${q \over {4\pi {\varepsilon _0}}} - {1 \over a}$$
C
$${q \over {4\pi {\varepsilon _0}}}\left( {{1 \over R} - {1 \over a}} \right)$$
D
$${q \over {4\pi {\varepsilon _0}}} - {1 \over R}$$
2
WB JEE 2021
+1
-0.25
Three infinite plane sheets carrying uniform charge densities $$-$$ $$\sigma$$, 2$$\sigma$$, 4$$\sigma$$ are placed parallel to XZ-plane at Y = a, 3a, 4a respectively. The electric field at the point (0, 2a, 0) is
A
$${{5\sigma } \over {2{\varepsilon _0}}}\widehat j$$
B
$$- {{7\sigma } \over {2{\varepsilon _0}}}\widehat j$$
C
$${\sigma \over {2{\varepsilon _0}}}\widehat j$$
D
$${{5\sigma } \over { - 2{\varepsilon _0}}}\widehat j$$
3
WB JEE 2021
+1
-0.25
Two point charges +q1 and +q2 are placed a finite distance d apart. It is desired to put a third charge q3 in between these two charges, so that q3 is in equilibrium. This is
A
possible only if q3 is negative.
B
possible only if q3 is positive.
C
possible irrespective of the sign of q3.
D
not possible at all.
4
WB JEE 2020
+1
-0.25
As shown in the figure, a point charge q1 = + 1 $$\times$$ 10-6 C is placed at the origin in xy-plane and another point charge q2 = + 3 $$\times$$ 10-6 C is placed at the coordinate (10, 0).

In that case, which of the following graph(s) shows most correctly the electric field vector in Ex in x-direction?
A
B
C
D
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