Question

Please answer the following

Chapter 21, Problem 57 Two circular loops of wire, each containing a single turn, have the same radius of 3.40 cm and a common center. The planes of the loops are perpendicular. Each carries a current of 1.50 A. What is the magnitude of the net magnetic field at the common center? Number Units the tolerance is +/-5% Click if you would like to Show Work for this question: Open Show Work

Answer 1

Magnetic field at the center of a wire, B = _$\mu$oI/2R
The magnitude of the magnetic field due to the second wire is same as B, but the direction is perpendicular to the first.
So the net field at the center, Bn = _$\mu$oI/2R $\hat{i}$ + _$\mu$oI/2R $\hat{j}$
Magnitude of the net magnetic field, |Bn| =  _$\mu$oI/2R x SQRT[1 + 1]
=  _$\mu$oI/2R x SQRT[2]
= (4$\pi$ x 10^-7 x 1.5) / (2 x 3.4 x 10^-2)] x SQRT[2]
= 3.92 x 10^-5 T