Chapter 20, Problem 7Q

To determine

Effect on a compass in terms of current, including if they are ac or dc. The magnetic field due to current in wire your home can affect a compass.

Answer to Problem 7Q

Solution:

Magnetic field produced by dc current, can deflect the magnetic compass needle.

Magnetic field produced by Ac current, can’t deflect the magnetic compass.

Explanation of Solution

Introduction:

$\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$

Where $m$ magnetic charge is $\overrightarrow{B}$ is magnetic field $\overrightarrow{\tau }$ is torque

DC: direct current which does not change the direction of current with time. DC current currying wire produced magnetic field. Which does not change with time. Invariable magnetic field will produce net torque on

Magnetic needle which can defect the needle.

Typical current in a house circuit is AC (alternating current), which frequency is $60\text{Hz}$, AC current produce variable magnetic field. This magnetic field change its direction $60$ times in just $1$ second.

Hence magnetic force on magnetic needle also change $60$ times in just $1$ second. Due to finite moment of inertia of magnetic needle can not change its orientation, the average force or average torque on magnetic needle is zero. Hence magnetic needle does not deflect.