A spherical e/3 balloon contains a charge +Q uniformly distributed over its surface. When it has a diameter D, the electric field at its surface has magnitude E. If the balloon is not blown up to thrice this diameter without changing the charge, the electric field at its surface is:. A. 4E.
B. 2E.
C. E.
D. E/2.
F. E/4.

Complete Question

A spherical e/3 balloon contains a charge +Q uniformly distributed over its surface. When it has a diameter D, the electric field at its surface has magnitude E. If the balloon is not blown up to thrice this diameter without changing the charge, the electric field at its surface is:________.

A. 4E.

B. 2E.

C. E.

D. E/2.

E  E/9

F. E/4.

The correct option is  E

Explanation:

From the question we are told that

    The  charge on the spherical balloon is  

    The diameter of the spherical balloon is  D  

     The magnitude of the electric field at the surface is  E  

Generally the electric field at the surface of the sphere is  mathematically represented as

where r is  the radius which can be represented as  

So  

Now when the diameter become thrice its original values the magnitude of  the   electric field becomes

=>      

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