Question

Consider a $10\,cm$ long portion of a straight wire carrying a current of $10\,A$ placed in a magnetic field of $0.1\,T$ making an angle of ${53^o}$ with the wire. What magnetic force does the wire experience?

Answer 1

In magnetism, when a current carrying wire is placed in a magnetic field it experiences a magnetic force which depends upon the magnitude of current, the length of wire and the magnetic field in which current carrying wire is placed, we will use the general formula of magnetic force and will calculate the magnitude of force according to given value of parameters.

Formula Used:
Force on a current carrying wire placed in a magnetic field is given by,
$F = i\vec L \times \vec B$
where “$i$” is the current $L$ length of wire having a vector cross product with magnetic field $B$.
If $\theta$ is the angle between wire length and magnetic field then magnetic force is calculated as,
$F = iBL\sin \theta$

Complete step by step answer:
Magnetic force is a consequence of electromagnetic force and is caused due to the motion of charges. With this context, the magnetic force can be described as a force that arises due to interacting magnetic fields.As we have given in the problem that,
$L = 10\,cm = 0.1\,m$ Length of the wire
$i = 10\,A$ Current flowing in the wire
$B = 0.1\,T$ Magnetic field where wire is placed
$\theta = {53^o}$
$\Rightarrow \sin {53^o} = 0.8$
So, using the formula of magnetic force we have,
$F = iBL\sin \theta$
$\Rightarrow F = 1 \times 0.1 \times 0.8$
$\therefore F = 0.08\,N$

Hence, the current carrying wire placed in magnetic field will experience a magnetic force of magnitude $F = 0.08\,N$.

Note: It must be noted that, while solving the question the basic unit of conversions are used as $1cm = 0.1m$ and the SI unit of force is called Newton denoted by N. Also, a current carrying wire creates its own magnetic field and thus when placed in another magnetic field either the wire will be attracted or repelled by the experience of magnetic force between these two magnetic fields.