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 [2007]

Question

Smart Achievers · Accepted Answer

(2)

Let the charge per unit volume be $σ$ and $O$ be the centre of a uniformly charged solid sphere. Let us consider a uniformly charged sphere of negative charge density $σ$ having its centre at $O'$ . Also let $OO'$ be equal to $a$ .

Let us consider an arbitrary point $P$ in the small sphere. The electric field due to charge on the big sphere using Gauss's theorem ${\vec{E}}_{1} = \frac{σ}{3 ε_{0}} {\vec{r}}_{1}$

Also the electric field due to the small sphere

${\vec{E}}_{2} = \frac{σ}{3 ε_{0}} {\vec{r}}_{2}$

$∴$ $The total electric field$

$\vec{E} = {\vec{E}}_{1} + {\vec{E}}_{2} = \frac{σ}{3 ε_{0}} a$

Hence the electric field will have a finite non-zero value which will be uniform.

Solution

Q.
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 [2007]

1 zero everywhere

2 non-zero and uniform

3 non-uniform

4 zero only at its center

Want Us to Email you About Special Offers & Updates?