Question

Fo 4. (10 points) A 2.0 m conductor is formed into a square and placed in the horizontal a-pl ane. A magnetic field is oriented 30.0° above the horizontal with a strength of 2.0 T. What is the magnetic flux through the conductor? A) 0.43 T- m2 B) 4.0 T- m2 C) 0.5 T, m?, D) 0.25 T-m A. si

Answer 1

The magnetic flux of a uniform magnetic field through a surface is given by

Φ=BAcos(θ)=BAcos⁡(θ)

Where B is the strength of the field, A is the area of the surface, and θ is the angle the magnetic field makes with the direction normal to the surface.

In this case, the vertical direction is normal to the surface. If the magnetic field makes a 30.0-degree angle with respect to the horizontal, then it is 60.0 degrees from the vertical.

The 2.0-m wire would form 0.5-meter-long sides of the square, so the area enclosed by the square is

A=L^2=(0.5 m)^2=0.25 m^2.

The flux through the square is then

Φ=BAcos(θ)=2.0 T×0.25 m^2×cos(60°)=0.25T⋅m^2

So the write answer is (d)