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**Forces between a Charge and a Bar Magnet**

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Concepts and ReasonThis problem can be solved using the following concepts: magnetic force, magnetic field and ferromagnetic material.

To determine the right option, first use expressions for magnetic force or torque.

To find the right option, you can use the expression magnetic force.

To find the right option, you can use concept ferromagnetism.

FundamentalsHere’s how to define magnetic force:

[katex]\vec F = q\left( {\vec v \times \vec B} \right)[/katex]

Here, the magnetic force (equa_tag_1) is used.

Below is the expression for torque:

[katex]\vec \tau = \vec r \times \vec F[/katex]

Here, the torque value is [katex]\vec \tau[/katex].

Ferrimagnets are magnetic materials with similar properties to iron. They can be permanently magnetized.

(A)These are the wrong options

* 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.

Below is the formula for magnetic force:

[katex]\vec F = q\left( {\vec v \times \vec B} \right)[/katex]

The charge is now stationary. The velocity is therefore zero.

The magnetic force is also zero since the velocity is zero.

[katex]F = 0[/katex]

Below is the expression for torque:

[katex]\vec \tau = \vec r \times \vec F[/katex]

The magnetic force is therefore zero. The above expression shows that there is no torque acting upon the magnet.

The correct choice is, therefore:* No torque at all.(B)These are incorrect expressions

* [katex]- \hat i[/katex]

* [katex]+ \hat j[/katex]

* [katex]- \hat j[/katex]

* [katex]+ \hat k[/katex]

The magnetic field direction in a bar magnet is from the North to the South Pole. Here, the magnetic field direction is [katex]- \hat j[/katex].

The charge moves in [katex]+ \hat i[/katex]

Below is the formula for magnetic force:

[katex]\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}[/katex]

The magnetic force is at [katex]- \hat k[/katex].

The correct choice is therefore,* [katex]- \hat k[/katex](C)These are the wrong options

* 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.

An induced magnetic field will form on the nail when there is no charge and an iron nail instead.

Near the bar, the nature of the pole inducing will be the opposite. Therefore, a magnet will induce a north pole near the south pole and vice versa.

The correct choice is, therefore:* Whichever pole of the magnet is closest to the magnet will be attracted to the iron.