If the potential at the center of a uniformly charged sphere of radius R is V then electric field at a distance r from the center of sphere will be ` ( r lt R ) ` : -

Options

A. ` (VR ) /( r ^ 2 ) `
B. ` ( 2 Vr ) /(3 R ^ 2 ) `
C. `( 2 VR ) /( r ^ 2 ) `
D. ` ( VR ) /( R^ 2 + r ^ 2 ) `

Answer

B

Explanation

Potential at the center of a uniformly charged sphere is given by
`V = ( 3 Q ) /( 8pi in _ 0 R ) ` where Q is change on sphere,
` k Q = ( 2 vR ) /( 3 ) `
For a inside point hollow sphere behaves like a point charge, placed at centre hence electric field, ` E = ( kQr ) /( R^ 3 ) = ( 2 vr ) /( 3 R^ 2 ) `