Question

You hold a wire coil so that the plane of the coil is perpendicular to a magnetic field vector B. Vector Bis kept constant but the coil is rotated so that the magnetic field, vector B , is now in the plane of the coil. How will the magnetic flux through the coil change as the rotation occurs?

Check all that apply.

The flux is unchanged because the magnitude of vector B is constant.

The flux increases because the angle between vector B and the coil's axis changes.

The flux decreases because the angle between vector B and the coil's axis changes.

The flux is unchanged because the area of the coil is unchanged.

 

Answer 1

Concepts and reason

The concepts used to solve this problem are changes in magnetic flux. When the angle between the plane of the coil and the magnetic field vector is perpendicular to each other, more magnetic flux passes through the coil. First, the plane of the coil is perpendicular to the magnetic field vector. When the coil is then rotated in the magnetic field, the angle between the coil plane and the magnetic field vector decreases due to the rotation.

Fundamentals

Magnetic flux is the number of magnetic field lines passing through a given area. The expression for magnetic flux through a coil is:

\(\phi=N(\vec{B} \cdot \vec{A})\)

Here, \(\phi\) is the magnetic flux through the coil, \(\vec{B}\) is the magnetic field vector, \(\mathrm{N}\) is the number of turns of the coil, and \(\vec{A}\) is the area vector of the coil. The expression for magnetic flux through the coil in scalar product form is:

\(\phi=B A N \cos \theta\)

Here, \(\theta\) is the angle between the perpendicular to the coil plane and the magnetic field vector.

The expression for magnetic flux through a coil is:

\(\phi=B A N \cos \theta\)

Magnetic flux through a coil depends on the magnitude of the magnetic field through the coil, area of the coil, number of turns of the coil, and the angle between the plane perpendicular to the coil (Area Vector) and the magnetic field vector. The amount of magnetic flux through the coil increases with an increase in the magnitude of the magnetic field, area of the coil, number of turns of the coil. It decreases with the increase in the angle between the plane perpendicular to the coil and the magnetic field vector.

Magnetic flux is the product of the average magnitude of a magnetic field and the perpendicular area of the coil through which it passes.

Rewrite the expression for magnetic flux through the coil \(\phi=B A N \cos \theta\)

As the angle \(\theta\) increases, the value of \(\cos \theta\) decreases from a maximum of 1 (when the plane of the coil is parallel to the magnetic field vector) to 0 (when the plane of the coil is perpendicular to the magnetic field vector). Keeping other quantities constant increases the value of \(\cos \theta\) decreases the magnetic flux through the coil.

The maximum value for cosine is 1, and the minimum value is \(0 .\) Keeping the other quantities fixed, the angle between the plane of the coil and the magnetic field vector B determines the amount of magnetic flux through the coil.

The flux decreases because the angle between vector B and the coil’s axis changes.