A $0.1m$ long conductor carrying a current of $50A$ is perpendicular to a magnetic field of $1.21mT$. The mechanical power to move the conductor with a speed of $1m{s}^{-1}$ is

1. $0.25mW$

2. $6.05mW$

3. $0.625W$

4. $1W$

The correct option is B

$6.05mW$

Step 1. Given data:

Length of the conductor = $0.1m$

Current = $50A$

Intensity of magnetic field = $1.21mT$

Speed = $1m{s}^{-1}$

Step 2. Formula used:

The angle between the magnetic field and the length of the conductor plays a significant role.

In order to experience maximum force, the conductor should be kept perpendicular to the magnetic field i.e., the angle between the length of the conductor and the magnetic field should be 90°.

The force on a current-carrying wire is maximum only when the wire is perpendicular to the direction of the magnetic field.

It is minimum, that is, no force acts on the conductor when it is parallel to the magnetic field.

Mechanical power required = electrical power expended due to the induced emf

$P_m=\left(F.v\right)=\left(B.I.L\sin \left(\theta \right)*v\right)\cos \varphi ...............\left(1\right)$

Where $Fisforce,visvelocity,Bismagneticfield,Iiscurrent,Lislength$

$$\begin{gathered} \theta istheanglebetweenmagneticfieldandcurrent \\ \varphi istheanglebetweenforceandvelocity \end{gathered}$$

As the angle between the magnetic field and length is $90°$. and $\sin 90°=1$, Hence equation $\left(1\right)$ becomes

$P_m=\left(B.I.L\right)\times v.....\left(1\right)$

Where $P_m=$Mechanical power required, $B=$Intensity of the magnetic field, $L=$Length of the conductor, $v=$speed, $I=$Current,

Step 3. Calculations:

Putting all the known values in the equation $\left(1\right)$. we get

$$\begin{gathered} P_m=\left(0.00121\times 0.1\times 1\right)\times 50 \\ =6.05mW \end{gathered}$$

Thus, option B is the correct option.