MCQ
The electrostatic potential on the surface of a charged conducting sphere is $100 V$ . Two statments are made in this regard: $S_1$ : At any point inside the sphere, electric intensity is zero. $S_2$ : At any point inside the sphere, the electrostatic potential is $100 V$ . Which of the following is a correct statement?
  • A
    $S_1$ is true but $S_2$ is false.
  • B
    Both $S _1 \& S_2$ are false.
  • $S_1$ is true, $S_2$ is also true and $S_1$ is the cause of $S_2$.
  • D
    $S _1$ is true, $S _2$ is also true but the statements are independant.

Answer

Correct option: C.
$S_1$ is true, $S_2$ is also true and $S_1$ is the cause of $S_2$.
We know, the electric field intensity $E$ and electric potential $V$ are related $\text{E}=\frac{\text{dV}}{\text{dr}}$.
If electric field intensity $E= 0$, then $\frac{\text{dV}}{\text{dr}}=0$. It means, $E = 0$ inside the charged conducting sphere causes uniform potential inside the sphere. Hence uniform electrostatic potential $100 V$ will be at any point inside the sphere.
Important points:
  1. The electric field zero does not necessary imply that electric potential is zero. E.g., the electric field intensity at any point inside the charged spherical shell is zero but there may exist non$-$zero electric potential.
  2. If two charged particles of same magnitude but opposite sign are placed, the electric potential at the midpoint will be zero but electric field is not equal to zero.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A particle is travelling $4$ times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is $2: 1,$ the mass of the particle is
Two small spheres each carrying a charge q are placed r metre apart. If one of the spheres is taken around the other one in a circular path of radius r, the work done will be equal to
Glass has refractive index $\mu $ with respect to air and the critical angle for a ray of light going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, the corresponding angle of refraction is
Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is
In a certain arrangement, a proton does not get deflected while moving through a magnetic field region. Under what condition is it possible?
Three charge $q$, $Q$ and $4q$ are placed in a straight line of length $l$ at points distant $0,\,\frac {l}{2}$ and $l$ respectively from one end. In order to make the net froce on $q$ zero, the charge $Q$ must be equal to
A magnetic needle lying parallel to a magnetic field requires $W$  units of work to turn it through $60°$ . The torque required to maintain the needle in this position will be
$A$ luminous point object is moving along the principal axis of a concave mirror of focal length $12\, cm$ towards it. When its distance from mirror is $20\, cm$ its velocity is $4\, cm/s$. The velocity of the image in $cm/s$ at that instant is :
A parallel beam of light travelling in water (refractive index $= 4/3$) is refracted by a spherical air bubble of radius $2\,cm$ situated in water. Assuming the light rays to be paraxial, the position of the image due to refraction at the first surface is
A point charge of $2.0\; \mu \,C$ is at the centre of a cubic Gaussian surface $9.0\; cm$ on edge. What is the net electric flux through the surface?