Question

Three long parallel wires are 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 6.80 A , but its direction in wire M is opposite to that in wires N and P

Determine the magnitude of the magnetic field at the midpoint of the line between wire M and wire N.

Express your answer using two significant figures.

Determine the angle of the magnetic field at the midpoint of the line between wire M and wire N.

Express your answer using two significant figures.

Answer 1

a) Magnetic field due to wire M and N,

B_MN = B due to M + B due to N

= u0i/(2piL/2) - u0i/(2piL/2) = 2e-7*6.8/(0.038/2) - 2e-7*-6.8/(0.038/2)

= 0.00014316 T

B due to P will be perpendicular to the above field as P lies of perpendicular bisector of line joining M and N.

B_P =  u0i/(2pi*L sin 60 degree)

= 2e-7*6.8/(0.038*sin 60 degree)

= 0.000041326 T

Net magnetic field = sqrt(B_MN^2+B_P^2) = sqrt(0.00014316^2+0.000041326^2)

= 0.00015 T answer

b) angle = 360 degree - 30 degree + 16 degree

= 330 degree + arctan(0.000041326/0.00014316)

= -14 degree or 346 degree in two sig fig 350  answer