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Magnetic Fields due to Electric Current — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMagnetic Fields due to Electric Current3 Marks
Question
A rectangular loop of wire hanging vertically with one end in a uniform magnetic field $\vec{B}$, supports a small block of mass $m . \vec{B}$ points into the page in the shaded region of below figure. For what current I in the loop would the magnetic force exactly balance the downward gravitational force?
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Answer

The magnetic force on the horizontal segment of the loop inside the field must be upward to balance the downward gravitational force.
With $\vec{B}$ pointing into the page, the current in that segment must be toward the right so that $\vec{F}=\vec{L} \times \vec{B}$ on that segment points upward.
That is, the current in the loop must be clockwise.
Taking $L=a, F=l a B$
$\therefore laB = mg$
$\therefore I =\frac{m g}{a B}$
is the required expression for the current.

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