Question

A circular loop of radius R is kept in a uniform magnetic field pointing perpendicular into the plane of paper.
When a current I flows in the loop, the tension produced in the loop is
1)BIR
2)BIR/2
3)2BIR
4)ZERO

Answer 1

Answer on Question # 69906, Physics / Electromagnetism

Question. A circular loop of radius $R$ is kept in a uniform magnetic field pointing perpendicular into the plane of paper. When a current $I$ flows in the loop, the tension produced in the loop is

1) $BIR$; 2) $BIR/2$; 3) $2BIR$; 4) $ZERO$.

Given.

B;

I;

R.

Find.

T.

Solution.

The loop has a curvature. As a result, when we take a small element $dl$ of the loop, the tension force applied to it from both the sides is at an angle (see figure).

From the figure, we have

$$dF = B \cdot I \cdot dl \cdot \sin \gamma = B \cdot I \cdot dl = B \cdot I \cdot R \cdot d\alpha,$$

where $dF = B \cdot I \cdot dl \cdot \sin \gamma$ – Ampere's force and $\gamma = 90{}^\circ \rightarrow \sin 90{}^\circ = 1$; $dl = R \cdot d\alpha$.

Finally

$$T d\alpha = dF = B \cdot I \cdot R \cdot d\alpha;$$

and

$$T = BIR.$$

Answer. $T = BIR$.

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