Question

Forces between a Charge and a Bar Magnet Learning Goal: To understand the forces between a bar magnet and 1. a stationary charge, 2. a moving charge, and 3. a ferromagnetic object. A bar magnet oriented along the y axis can rotate about an axis parallel to the z axis. Its north pole initially points along j

Answer 1

Concepts and reason

The concepts used to solve this problem are magnetic force, magnetic field, ferromagnetic materials, and torque.

Initially, use expression for magnetic force and torque to determine the correct option.

Then, use the expression for magnetic force to find the correct option.

Finally, use concept ferromagnetism to find the correct option.

Fundamentals

The expression for magnetic force is as follows:

$\vec F = q\left( {\vec v \times \vec B} \right)$

Here, the magnetic force is $\vec F$ , the charge is $q$ , the velocity is $\vec v$ , and the magnetic field is $\vec B$ .

The expression for the torque is given below:

$\vec \tau = \vec r \times \vec F$

Here, the torque is $\vec \tau$ , the distance vector is $\vec r$ , and the force is $\vec F$ .

The ferrimagnets are materials that have magnetic properties similar to those of iron. They can become permanently magnetized.

(A)

The incorrect options are,

• A torque due to charge attracting the north pole of the magnet.

• A torque due to charge attracting the south pole of the magnet.

• A torque only if one magnetic pole is slightly closer to charge than the other.

The expression for the magnetic force is given below:

$\vec F = q\left( {\vec v \times \vec B} \right)$

Here, the charge is stationary. Hence, the velocity is zero.

Since, the velocity is zero the magnetic force is zero.

$F = 0$

The expression for the torque is given below:

$\vec \tau = \vec r \times \vec F$

Here, the magnetic force is zero. Hence, from the above expression we get there is no torque acting on the magnet.

Hence, the correct option is,

• No torque at all.

(B)

The incorrect expressions are,

• $- \hat i$

• $+ \hat j$

• $- \hat j$

• $+ \hat k$

In a bar magnet the direction of the magnetic field is from north to South Pole. Hence, here the direction of magnetic field is in $- \hat j$ direction.

The charge moves in $+ \hat i$ direction. Hence, the direction of velocity vector is $+ \hat i$ .

The expression for the magnetic force is given below:

$\begin{array}{c}\\\vec F = q\left( {v\hat i \times - B\hat j} \right)\\\\ = qvB\left( {\hat i \times - \hat j} \right)\\\\ = - \hat k\\\end{array}$

The magnetic force is in $- \hat k$ direction.

Hence, the correct option is,

• $- \hat k$

(C)

The incorrect options are,

• The magnet will experience a torque due to the iron attracting its north pole.

• The magnet will experience a torque due to the iron attracting its south pole.

• Whichever pole of the magnet is closest to the magnet will be repelled from the iron.

When instead of a charge an iron nail at that point there will be an induced magnetic field on the nail.

The nature of the pole induced will be opposite near to the bar. Thus, a north pole is induced near south pole of the magnet and vice versa.

Hence, the correct option is,

• Whichever pole of the magnet is closest to the magnet will be attracted to the iron.

Ans: Part A

The magnet will experience no torque at all.

Part B

The direction of magnetic force is ${\bf{ - \hat k}}$ .

Part C

Whichever pole of the magnet is closest to the magnet will be attracted to the iron.