1
AIPMT 2009
+4
-1
Three concentric spherical shells have radii a, b and c (a < b < c) anf have surface charge densities $$\sigma$$, $$-$$$$\sigma$$ and $$\sigma$$ respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a + b, we have
A
VC = VB $$\ne$$ VA
B
VC $$\ne$$ VB $$\ne$$ VA
C
VC = VB = VA
D
VC = VA $$\ne$$ VB
2
AIPMT 2009
+4
-1
The electric potential at a point (x, y, z) is given by V = $$-$$x2y $$-$$ xz3 + 4

The electric field at that point is
A
$$\overrightarrow E = \widehat i2xy + \widehat j\left( {{x^2} + {y^2}} \right) + \widehat k\left( {3xz - {y^2}} \right)$$
B
$$\overrightarrow E = \widehat i{z^3} + \widehat jxyz + \widehat k{z^2}$$
C
$$\overrightarrow E = \widehat i\left( {2xy - {z^3}} \right) + \widehat jx{y^2} + \widehat k3{z^2}x$$
D
$$\overrightarrow E = \widehat i\left( {2xy + {z^3}} \right) + \widehat j{x^2} + \widehat k3x{z^2}$$
3
AIPMT 2008
+4
-1
A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

A
E along KO
B
3E along OK
C
3E along KO
D
E along OK
4
AIPMT 2008
+4
-1
The electric potential at a point in free space due to charge Q coulomb is Q $$\times$$ 1011 volts. The electric field at that point is
A
$$4\pi {\varepsilon _0}Q \times {10^{20}}$$ volt/m
B
12$$\pi$$0Q $$\times$$ 1022 volt/m
C
$$4\pi {\varepsilon _0}Q \times {10^{22}}$$ volt/m
D
$$12\pi {\varepsilon _0}Q \times {10^{20}}$$ volt/m
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