Question

A wire on a circuit board has a length l=3.9mm and carries a current i=2.25μA in the positive

y direction. A nearby circuit element generates a magnetic field in the vicinity of the wire.

A) Determine the direction of the magnetic field.

B) Calculate the magnitude of the magnetic field.

Answer 1

The direction of the magnetic field is in the positive z-direction. The magnitude of the magnetic field is 5.77 * 10^-4 T.

Step-by-step explanation:

A) To determine the direction of the magnetic field, you can use the right-hand rule. According to the right-hand rule, if you point your right thumb in the direction of the current (positive y-direction), your fingers will curl in the direction of the magnetic field. Therefore, the direction of the magnetic field is in the positive z-direction.

B) To calculate the magnitude of the magnetic field, you can use the formula F = I * B * l, where F is the force, I is the current, B is the magnetic field, and l is the length of the wire. In this case, the force is per unit length, so you can rearrange the formula to B = F / (I * l). Substituting the given values, the magnitude of the magnetic field is B = (2.25 * 10^-6 A) / (3.9 * 10^-3 m) = 5.77 * 10^-4 T.