A thin, straight test conductor of length carries a variable current and is placed in…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A thin, straight test conductor of length ℓ carries a variable current I and is placed in a uniform magnetic field of fixed magnitude B. The conductor can be rotated so that the angle θ between the current direction and the magnetic field is continuously adjustable from 0∘ to 180∘.
(a) Show that the magnitude of the magnetic force on the conductor can be written in the form F(θ)=Fmaxsinθ, where Fmax is a constant to be determined in terms of I, ℓ, and B. Provide a clear logical sequence leading to this functional dependence without explicitly citing any standard formulas.
(b) Using the result from part (a), analytically determine the values of θ at which the magnitude of the magnetic force changes most rapidly with respect to θ. Support your answer with appropriate reasoning.
(c) Sketch a graph of F versus θ for 0∘≤θ≤180∘. On your sketch clearly indicate the angles identified in part (b) and explain how the slope of the graph at those points is consistent with your analytical result.
(d) Suppose the current in the conductor is now doubled while all other quantities remain the same. Describe how the graph you sketched in part (c) would be altered, and explain how this change is reflected in the functional dependence derived in part (a).