Question

Calculate the magnetic force per unit length on a wire carrying a current of 10 A and making an angle of ${45^^\circ }$ with the direction of a uniform magnetic field of $0.2T$.
(A) $2\sqrt 2 N{m^{ - 1}}$
(B) $\dfrac{2}{{\sqrt 2 }}N{m^{ - 1}}$
(C) $\dfrac{{\sqrt 2 }}{2}N{m^{ - 1}}$
(D) $4\sqrt 2 N{m^{ - 1}}$

Answer 1

Hint
Magnetic force arises in a wire between electrically charged particles because of their motion. This force depends on the strength of the magnetic field generated and the length of the wire, simultaneously.
Formula used: $F = BIl\sin \theta $, where F is the magnetic force on the current-carrying wire, B is the magnetic field strength, l is the length of the wire and $\theta $ is the angle the current makes with the direction of the magnetic field.

Complete step by step answer
The question asks us to calculate the force per unit length on a current-carrying wire under the influence of a magnetic field. The data provided to us includes:
Current flowing in the wire $I = 10$A
Angle between current flow and magnetic field $\theta = 45^\circ $
Strength of the magnetic field $B = 0.2T$
We know that the magnetic force on a current-carrying wire is given as:
$F = BIl\sin \theta $
To get the force per unit length, we divide both sides by a factor of l to get:
$\dfrac{F}{l} = BI\sin \theta $
Putting the given values in this equation gives us:
$\dfrac{F}{l} = 0.2 \times 10 \times \sin 45^\circ $
$ \Rightarrow \dfrac{F}{l} = 2 \times \dfrac{1}{{\sqrt 2 }} = \dfrac{2}{{\sqrt 2 }}$N/m
This is the value of the magnetic force per unit length, and thus the correct answer is option B.

Note
A magnetic field is a vector field and describes the magnetic influence on moving electric charges, electric currents, and magnetized materials. The relation between the magnetic field strength and the current flowing through it is given by the Biot-Savart Law. The magnetic force generated by this field finds applications in many day-to-day appliances like our televisions, and radio sets. Even the computer uses magnetic force to store data on a rotating disk.