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JEE PHYSICS MCQ: ELECTRIC POTENTIAL AND CAPACITANCE

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Application +4 | -1

Two concentric hollow spherical shells have radii

\text{r}

and

\text{R} (\gg \text{r}).

A charge

\text{Q}

is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

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Correct option: A

\frac{\mathrm{Q}(\mathrm{R}+\mathrm{r})}{4 \pi \varepsilon_0\left(\mathrm{R}^2+\mathrm{r}^2\right)}

Option A is correct because the electric potential at the center is calculated by summing the potentials due to each spherical shell, considering their respective charges and radii, and using the condition of equal surface charge densities.

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The potential at a point distance

x

(measured in

\mu \mathrm{m}

) due to some charges situated on the

x

axis is given by

V(x)=\frac{20}{x^2-5} \mathrm{V}

. The electric field at

x=5 \mu \mathrm{m}

is given by: A parallel plate capacitor is connected to a 5V battery and charged. The battery is then disconnected and a glass slab is introduced between the plates. Then, the quantities that decrease are A conducting sphere of radius

R

is given a charge

Q

. The electric potential and the electric field at the centre of the sphere respectively are Two capacitors when connected in series have a capacitance of

3\mu F,\,

and when connected in parallel have a capacitance of

16\mu F

. Their individual capacities are Statement-1: If temperature is increased, the dielectric constant of a polar dielectric decreases whereas that of a non-polar dielectric does not change significantly.
Statement-2: The magniude of dipole moment of individual polar molecule decreases significantly with increase in temperature. An electric dipole when placed in a uniform electric field

E

will have minimum potential energy, if the positive direction of dipole moment makes the following angle with

E