Question

Two long straight wires are parallel and 8.6 cm apart. They are to carry equal currents such that the magnetic field at a point halfway between them has magnitude 370 µT. (a) Should the currents be in the same or opposite directions? (b) How much current is needed?

Answer 1

(a) The current should be in opposite direction

(b) The current needed is 39.8 A

Step-by-step explanation:

Part (a)

Based, on right hand rule, the current should be in opposite direction

Part (b)

given;

strength of magnetic field, B = 370 µT

distance between the two parallel wires, d = 8.6 cm

`B = (\mu_oI)/(2\pi R)`

At the center, the magnetic field strength is twice

`B_c = 2((\mu_oI)/(2\pi R)) =( \mu_oI)/(\pi R)`

R = d/2 = 8.6/2 = 4.3 cm = 0.043 m

`B_c = ( \mu_oI)/(\pi R)\\\\I = (B_c\pi R)/(\mu_o) = (370 *10^(-6)* \pi *0.043)/(4\pi *10^(-7))\\\\I = 39.8 \ A`

Therefore, current needed is 39.8 A