Question

Two long straight wires are parallel and 9.3 cm apart. They are to carry equal currents such that the magnetic field at a point halfway between them has magnitude 290 µT. (a) Should the currents be in the same or opposite directions? (b) How much current is needed?

Answer 1

A) OPPOSITE

B) I =33.71 A

Step-by-step explanation:

a) we know that magnetic field B is given by

`B =( \mu_0 I)/(2\pi R)`

for having magnetic field value same at center point, the both wire must be parallel and distance between from the centre point for bothe wire should be same. so to get non zero value the magnetic field must be in same direction, therefore current must be in opposite direction.

b) The magnetic field at halfway point between the wire

at the center magnetic field B_2 is equal to twice as B_1

B_2 =2* B_1

`B_2 =(\mu_0 I)/(2\piR)`

`B_2 =(\mu_0 I)/(2\piR)`

`I = (\pi R B_2)/(\mu_O)`

R = 4.65 cm

`\mu_O = 4\pi * 10^(-7)` T. m/A

`I = (\pi *0.0465(290*10^(-6)))/(4*\pi 10^(-7))`

I =33.71 A