Answer to Question #314529 in Electricity and Magnetism for ali

Question

1. A long, straight conductor carries a current of 200 A. At what distance from the conductor is the magnetic field

caused by the current equal to the Earth’s magnetic field?

2. A power cable contains two long parallel conductors placed 1.5 cm apart. It carries a current of 125 A to a 40 hp

electric motor. Find the force exerted on a 2.0 m length of one conductor?

3. A coil used to produce a magnetic field for an electron beam experiment has a radius of 15 cm and has 300

turns. What current is needed to produce a magnetic field of 5.0 x 10-3 T?

Answer 1

(1)

Magnetic field

$B=\frac{\mu_0 I}{2\pi r}$

$r=\frac{4\pi\times10^{-7}\times200}{2\pi\times 5\times10^{-5}}=0.8m$

(2) force

$F=\frac{\mu i_1i_2}{2\pi r}$

$$F=\frac{4\times3.14\times 125\times125}{2\times3.14\times0.015}=2.08\times10^{6}N$$

(3) magnetic field

$B=\frac{\mu_0Ni}{2r}$

$i=\frac{5\times10^{-3}\times2\times0.15}{300\times4\times3.14\times10^{-7}}=3.98A$