Discussion Forum



1)

Consider a uniform spherical charge distribution of radius R1   centred at the origin O. In this distribution, a spherical cavity of radius R2, centred at P with distance OP=a=R1- R2 (see figure) is made. If the electric  field inside the cavity at position r is  E(r), then the correct statements is /are

 93202129_p5.JPG


A) E is uniform , its magnitude is independent of $R_{2}$ but its direction depends on r

B) E is uniform , its magnitude depends on $R_{2}$ and its direction depends on r

C) E is uniform , its magnitude is independent of 'a' but its direction depends on a

D) E is uniform and both its magnitude and direction depends on a

Answer:

Option D

Explanation:

The sphere with cavity can be assumed as a complete sphere with positive charge of radius R1 + another complete sphere with negative charge and radius R2.

$E_{+}\rightarrow$  E due to total positive charge

$E_{-}\rightarrow$     E due to total negative charge.

                       $E=E_{+}+E_{-}$

 If  we calculate it at P,  then E-  comes out to be zero.

 $\therefore$                       $E=E_{+}$

 and     $E_{+}=\frac{1}{4\pi \epsilon_{0}}\frac{q}{R_1^3}(OP)$   , in the direction of OP.

 Here, q is total positive charge on whole sphere.

 It is in the direction of OP or a.

 Now, inside the cavity electric field comes out to be uniform at any point. This is a standard result.