   Chapter 25, Problem 31P Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Solutions

Chapter
Section Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

A small object with electric dipole moment p → is placed in a nonuniform electric field E → = E ( x ) i ^ . That is, the field is in the x direction, and its magnitude depends only on the coordinate x. Let θ represent the angle between the dipole moment and the x direction. Prove that the net force on the dipole is F = p ( d E d x ) cos θ acting in the direction of increasing field.

To determine

To show: The net force on the dipole is F=p(dEdx)cosθ .

Explanation

Given Info: The dipole moment is p and the angle between the dipole moment and x -direction is θ .

Explanation:

Formula to calculate the potential energy stored in a dipole with dipole moment in electric field is,

U=pE=pEcosθ

Here,

E is the electric field.

p is the electric dipole moment.

Formula to calculate the net force on the dipole along the x -direction is,

F(x)=dUdx

Here,

F(x) is the net force on the dipole along the x -direction

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