Chapter 26, Problem 57A

To determine

To Explain: If the sign of the charge particles is change from positive to negative, so the directions of either or both of the fields have to be changed to keep the particles un-deflected.

Answer to Problem 57A

The direction of the magnetic field is opposite of the earlier direction.

Explanation of Solution

Introduction:

The magnetic field on the charged particle causes the particle to move in a circular motion. The magnetic force on the charged particle is equivalent to the centripetal force on the particle.

The equation for force can be written as

  $Bqv=\frac{m{v}^2}{r}$......(1)

Here, $B,q,v,m,r$ are the strength of the magnetic field, the charge of the ion, velocity of the particle, the mass of the ion, and radius of the path respectively.

If the sign of the charged particles is the changed from positive to negative without a change in the direction of the magnetic field, the particle will move to the left side or counterclockwise. To keep the particle unaltered, the force due to the electric field should be equal to force due to the magnetic field.

Conclusion:

Hence, the direction of the magnetic field is the opposite of the earlier direction.