Four identical straight steel wires P, Q, R and S lie inside the same uniform…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism

Problem

Four identical straight steel wires P, Q, R and S lie inside the same uniform magnetic field. Each wire has the same resistivity and cross-section but carries different currents and is oriented at different angles to the field as shown in the table below. Base values:

I_0 = 5\,\text{A}

L_0 = 0.20\,\text{m}

Wire	Current	Length in field	Angle with field
P	$I_0$	$L_0$	90°
Q	$1.5I_0$	$0.8L_0$	45°
R	$0.5I_0$	$1.2L_0$	30°
S	$2I_0$	$0.6L_0$	120°

All other physical conditions are identical. (a) Without evaluating the individual forces numerically, arrange the wires in the order of decreasing magnitude of magnetic force. Show clearly how you arrive at your ordering. (b) For wires P and Q, calculate the exact ratio

F_Q/F_P

of their forces. (c) The force on wire R is required to be doubled by changing only the angle it makes with the magnetic field. Determine the new angle (0° ≤ θ ≤ 180°) that will achieve this, keeping its current and length unchanged.

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