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
Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltages of the combination will be
A
$$3C,{V \over 3}$$
B
$${C \over 3},3V$$
C
$$3C,3V$$
D
$${C \over 3},{V \over 3}$$
3
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
$$\overrightarrow E = \widehat i\left( {2xy + {z^3}} \right) + \widehat j{x^2} + \widehat k3x{z^2}$$
4
AIPMT 2008
+4
-1
A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
A
$${1 \over 2}{\varepsilon _0}{E^2}$$
B
$${{{E^2}Ad} \over {{\varepsilon _0}}}$$
C
$${1 \over 2}{\varepsilon _0}{E^2}Ad$$
D
$${\varepsilon _0}EAd$$
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