PhysicsLAB: Practice with Ampere's Law

Ampere's Law is extremely useful in calculating the magnitude of magnetic fields when there is symmetry in the application. Remember that Ampere's Law is stated as

When applying Ampere's Law we must use an Amperian Loop which is a closed path with a specified direction to its circulation. Remember that µ_o equals 4p x 10^-7 Tm/A.

The following formulas are based on Ampere's Law:

Refer to the following information for the next three questions.

In the following diagram, all of the Amperian loops have a clockwise circulation. Each current equals 2 amps. Dots mean that the current is in the +z direction (out of the page) and crosses means that the current is in the -z direction (into the page).

Evaluate

for the currents in the blue circle.

Evaluate

for the currents in the green circle.

Evaluate

for the currents in the purple square.

Refer to the following information for the next six questions.

An infinitely long straight wire is carrying a current of 2 A in the +x direction.

What is the strength of the magnetic field at point P which is 10 cm from the top of the wire?

A second infinitely long wire, carrying 2 A of current in the +y direction, is now placed 10 cm to the left of P. What is the net magnetic field at P?

The two infinitely long wires are now oriented so that their current flow anti-parallel to each other. What is the net magnetic field at point P?

Will the two wires in the previous example attract or repel each other?

attractrepel

The second wire is replaced with a current carrying loop in the shape of a rectangle having dimensions 20 cm x 10 cm. The current present remains 2 A.

Will the forces on the sides of the rectangle result in its area increasing or decreasing?

increasingdecreasing

Calculate the net force on the rectangle.

Refer to the following information for the next two questions.

An infinitely long wire carrying 2 A of current in the positive x-direction skirts around point P in a semicircle of radius 5 cm.

What is the magnetic field at point P?

Point P is now moved to the center of two semi-circular arcs. The radius of the inner arc is 5 cm and the radius of the outer arc is 10 cm. What is the net B-field at P?