A straight aluminium rod of length carries a current while lying in a uniform…

PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

Problem

A straight aluminium rod of length

L

carries a current

I

while lying in a uniform magnetic field

B

. The rod can be rotated in its own plane so that the angle between the rod and the magnetic field can be set to any desired value. (i) Derive an expression for the ratio

\dfrac{F_{\theta}}{F_{90^{\circ}}}

, where

F_{\theta}

is the magnitude of the force when the rod makes an angle

\theta

with the field and

F_{90^{\circ}}

is the magnitude when the rod is perpendicular to the field. (ii) Using your expression, calculate the force on the rod when

\theta=45^{\circ}

, given that

I=10\,\text{A}

L=0.40\,\text{m}

, and

B=0.50\,\text{T}

. (iii) If the current is doubled and the angle is halved simultaneously, determine the new magnitude of the force and compare it (as a multiple) with the value obtained in part (ii).

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