MCQ
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is
  • A
    zero everywhere
  • non-zero and uniform
  • C
    non-uniform
  • D
    zero only at its center

Answer

Correct option: B.
non-zero and uniform
b
If a Gaussian surface is constructed within the cavity then by Gauss Law $\oint$ E. dS $=0$. This does not mean that $E =0$.

From the image, consider a point $P$ inside the cavity and let $\rho$ be the charge density. Then, after applying superposition principle the net electric field at point $P$ will be:

$E=\frac{\rho}{3 \epsilon_0} \vec{b}-\frac{\rho}{3 \epsilon_0} \vec{a}$

$=\frac{\rho}{3 \epsilon_0} \vec{r} \text { (Since } \vec{r}=\vec{b}-\vec{a} \text { ) }$

which for a given cavity is independent of the position of a point within the cavity.

Therefore, Electric field is non-zero and uniform within the cavity.

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

In the given circuit calculate potential difference between $A$ and $B$ ............... $\mathrm{V}$
A proton of mass $ 1.6  \times 10^{-27} kg$ goes round in a circular orbit of radius $0.10\, m$ under a centripetal force of $4  \times 10^{-13}\, N$. then the frequency of revolution of the proton is about 
Determine coefficient of performance of given temperature limit.

$T_{1}=27^{\circ} C$ [outside fridge]

$T_{2}=-23^{\circ} C$ [inside fridge]

The transconductance of a triode amplifier is $2.5 \,mili\, mho$ having plate resistance of $20 \, k \Omega$, amplification $10$. Find the load resistance........$ k \Omega$
A body takes $5$ minutes to cool from $90^oC$ to $60^oC$. If the temperature of the surroundings is $20^oC$, the time taken by it to cool from $60^oC$ to $30^oC$ will be ...... $\min.$
If the unit of force and length each be increased by four times, then the unit of energy is increased by.....$times$
Consider the following volume-temperature $( V - T )$ diagram for the expansion of $5$ moles of an ideal monoatomic gas.

Considering only $P-V$ work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$

[Use the given data: Molar heat capacity of the gas for the given temperature range, $C _{ v , m }=12 J K ^{-1} mol ^{-1}$ and gas constant, $R =8.3 J K ^{-1} mol ^{-1}$ ]

The temperature of the body is increased from $-73^o C\, to \,327^o C$, the ratio of energy emitted per second is :
Two capacitors $C_1$ and $C_2$ are connected in a cirucit as shown in figure. The potential difference $(V_A -V_B)$ is.....$V$
$P-V$ diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be