Question

The magnetic field at the center of a 1.0-cm-diameter loop is 2.5 mT.

Answer 1

Answer:

(a) The current in the wire is 19.89 A

(b) The distance from the wire is 0.159 cm

Explanation:

Given;

magnetic field, B = 2.5 mT

diameter of the wire, d = 1 cm

radius of the wire, r = 0.5 cm = 0.005 m

(a) The current in the wire is calculated as;

$I = \frac{2Br}{\mu_0} \\\\I = \frac{2\times 2.5 \times 10^{-3} \times 0.005 }{4\pi \times 10^{-7} } \\\\I = 19.89 \ A$

(b) The distance from the wire where the magnetic field is 2.5 mT is calculated as;

$B = \frac{\mu_0 I}{2\pi d} \\\\where;\\\\d \ is \ the \ distance \ from \ the \ wire\\\\d = \frac{\mu_0 I}{2\pi B} = \frac{4 \pi \times 10^{-7} \times 19.89}{2\pi \times 2.5 \times 10^{-3}} = 0.00159 \ m = 0.159 \ cm$