Chapter 20, problem 31: Rectangular Circuit Oriented with its Plane Parallel to Uniform Magnetic Field

Chapter 20, problem 31.

A rectangular x₁ cm by x₂ cm circuit carrying an x₃ A current is oriented with its plane parallel to a uniform x₄ T magnetic field (Figure 20.62, page 693).
(a) Find the magnitude and direction of the magnetic force on each straight segment of this rectangular circuit. Illustrate your answers with clear diagrams (F₁ = ?, F₂ = ?, F₃ = ?, F₄ = ?).
(b) Find the magnitude of the net force on the entire circuit (F_N = ?).
(c) Find the magnitude of the net torque on the entire circuit (τ = ?).

Solution

Given:

H = x₁ cm F₂ = ?L = x₂ cm
I = x₃ A

B = x₄ T

(a) F₁ = ?, F₂ = ?, F₃ = ?, F₄ = ?

(b) F_N = ?

(c) τ = ?

A = x₁ · x₂ cm²