Question

Two long parallel wire each carry 2.5 A in the same direction, with their centers 1.5 cm apart.

A. Find the magnetic field halfway between the wires.

B. Find the magnetic field at a point in the same plane as the wires, 1.5 cm from one wire and 3.0 cm from the other.

C. Find the force of interaction between the wires, and tell whether it’s attractive or repulsive.

Answer 1

a) if two wires carry the currents in same direction ,then at the midpint the magnetic fields due to two currents are in opposite direction

hence they will cancels

Net magnetic field is Bnet = B1-B2

B1 = B2

Then Bnet = 0 T half way between the wires

B) at a distance r1 = 1.5 cm from one wire and r2 = 3 cm from the other wire

then

B = B1+B2

B1 = mu_o*I1/(2*pi*r1) = (4*3.142*10^-7*2.5)/(2*3.142*1.5*10^-2) = 3.33*10^-5 T

B2 = mu_o*I1/(2*pi*r2) = (4*3.142*10^-7*2.5)/(2*3.142*3*10^-2) = 1.67*10^-5 T

B = B1+B2 = (3.33+1.67)*10^5 = 5*10^5 T

C) F = mu_o*i1*i2/(2*pi*d) = (4*3.142*10^-7*2.5*2.5)/(2*3.142*0.015) = 8.34*10^-5 T

since the currents are is same direction they will attract each oter