Physics

Problem

A straight aluminium rod of length

0.25\,\text{m}

carries a current of

15\,\text{A}

while placed in a uniform magnetic field of strength

0.80\,\text{T}

. The rod initially makes an angle of

45^{\circ}

with the magnetic field direction. (i) Derive an expression relating the initial field

B_1

, the initial angle

\theta_1

, the final field

B_2

and the final angle

\theta_2

if the magnitude of the magnetic force on the rod is to remain unchanged when the rod is rotated but the current is kept the same. (ii) Using the expression obtained, calculate the value of

B_2

required if the rod is rotated so that it now makes an angle of

30^{\circ}

with the field direction.

Intuitive explanation

The magnetic force on a current-carrying conductor depends on both the field strength and the sine of the angle between the current and field—this is the key to keeping force constant despite changing geometry. When you rotate the rod, you're weakening the "effective" perpendicular component of the field, so you need a stronger field to compensate. Set up the force equation at two different configurations and equate them to find the relationship between the field strengths and angles.

Intuitive explanation

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