Electric field intensities at two axial points of an electric dipole at distances 5 cm and 10 cm from its centre are ` 2.5 xx 10 ^( 4 ) N * C ^( - 1 ) and 2 xx 10 ^ 3 N * C ^ ( - 1 ) ` respectively. The dipole is placed in air. determine the length of the dipole.

Explanation

Suppose , the length of the electric dipole = `2l`.
We know,
` E = ( 1 ) /( 4pi in _ 0 ) * ( 2pr ) /( ( r^ 2 - l^ 2 ) ^ 2 ) `
According to the question,
`2.5 xx 10 ^ 4 = 9 xx 10 ^( 9) * (2p xx 0.05 ) /([(0.05 ) ^ 2 - l ^ 2 ]^ 2 ) " " `...(i)
and ` 2xx 10 ^( 3 ) = 9 xx 10 ^( 9) * ( 2p xx 0.1 ) /([ ( 0.1)^ 2 - l^ 2 ] ^ 2 ) " " `...(2)
Dividing (1) by (2) we get,
`1.25 xx 10 = ( 0.1) ^ 2 - l ^ 2 ]^ 2 xx 0.05 ) /( [ (0.05 ) ^ 2 - l ^ 2 ] ^ 2 xx 0.1 ) `
or, `25 = ([(0.1)^2 - l ^ 2 ] ^ 2 ) /( [ (0.05 ) ^ 2 - l ^ 2 ] ^ 2 ) ` or, ` 5 = (( 0.1 ) ^ 2 - l ^ 2 ) /( (0.05 ) ^ 2 - l ^ 2 ) `
or, ` 2l = 0.05 m `
` therefore ` The length of the electric dipole = 0.05 m.