A student calculates the magnetic force on a straight wire in two different—but…

PHYSICS · Subjective · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism

Problem

A student calculates the magnetic force on a straight wire in two different—but mathematically equivalent—ways: • Method 1: Multiply

I l B

and then include the factor

\sin\theta

. • Method 2: First find the component of the wire’s length perpendicular to the field,

l_\perp = l \sin\theta

, and then multiply

I l_\perp B

. In one or two sentences, explain why both methods produce the same numerical force value.