The Problem of the Magnitude of a Magnetic Field

magnitude of magnetic field

A loop wire in the form of the right triangle (see figure) carries a current of 10 A. A magnetic field of 2 T is directly parallel to AB. The length of AB is 3 m. Find the magnitude of the magnetic forces exerted on each side of the loop.

Solution:

1.Magnitude for AB side:

For the AB side, the current is parallel to the magnetic field. Thus, there is no force.

F_A_B = O N

2.Magnitude for BC side:

For the BC side, the current is perpendicular to the magnetic field. The length of BC is:

BC = AB × tan(60°) = 5.2 m
F_B_C = B × I × BC × sin(90°) = 104 N

3.Magnitude for AC side:

For the AC side, the angle between the current of the magnetic field is 60°. The length of the AC side is:

AC = AB / cos(60°) = 6 m

F_A_C = B × I × AC × sin(60°) = 104 N

magnitude of magnetic field example

Two long and straight wires are perpendicular to each other. The current in each wire is 6 A. Find the magnitudes of magnetic fields and the directions in points A and B, where v is 0.45 m, and h is 0.6 m.

Solution:

magnitude of magnetic force

Taking the sum of the values from above, we can find the magnitudes of the magnetic fields in points A and B:

magnitude of magnetic force equation

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