please make sure you have the right answer. Three long, parallel, straight wires

Question

please make sure you have the right answer. Three long, parallel, straight wires pass through the vertices of an equilateral triangle that has sides L = 13.0 cm, as shown in the figure below. A a dot indicates that the direction of the current is out of the screen and a cross indicates that the direction of the current is into the screen.

Each current is 20.0 A.

(a) Find the magnetic field at the location of the upper wire due to the currents in the two lower wires.

(b) Find the force per unit length on the upper wire.

magnitude ............. µT direction ............... toward the top - toward the bottom - toward the left - toward the right.

Explanation / Answer

part a )

from the geometry of the wires, the magnetic field vectors both are at an angle of 30 degree with the horizontal and their y component will cancel

B =(2uo*I/2pi*r ) * cos30 i

r = 13 cm = 0.13m

B = 4 x 10^-7 * 20 / 0.13

B = 6.154 x 10^-5 T = 61.54 uT

direction = toward the right

part b )

F/L = uo*I^2/2pi*d

by two wire

F/L = 2uo*I^2/2pid

F/L = 2 * 2 x 10^-7 * (20)^2 / 0.13

F/L = 1.23 x 10^-3 N/m

direction = towards the top

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