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Chapter 24: Q71P (page 715)

Starting from Eq. 24-30, derive an expression for the electric field due to a dipole at a point on the dipole axis.

Short Answer

Expert verified

E=12蟺蔚o鈰�pr3

Step by step solution

01

Understanding the concept

After reading the question, consider an electric dipole of charge 卤q to be separated by 鈥�诲鈥�.

The electric potential at a distance 鈥榬鈥� with angle 胃from the middle of the electric dipole is given as:

V=14蟺蔚o鈰�p鈥塩辞蝉鈥�胃r2,wherep=qd

滨蹿鈥�胃=0,肠辞蝉鈥�0=1

V=14蟺蔚o鈰�pr2

02

Step 2: Derive an expression for the electric field due to a dipole at a point on the dipole axis

According to the definition of a potential gradient,

E=鈭�鈭�V鈭�rE=鈭�p4蟺蔚od(r鈭�2)drE=+2脳p4蟺蔚or鈭�3E=12蟺蔚o鈰�pr3

Hence, the expression isE=12蟺蔚o鈰�pr3

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