Could somebody answer this question? You do not need to draw the vectors, wordin

Question

Could somebody answer this question? You do not need to draw the vectors, wording is fine.

Three long parallel wires are placed at the corners of an equalateral triangle of side length 7.5 cm as shown above. Each wire carries electric current. The bottom two wires carry current into the page and the top wire carries current out of the page.

a) Draw a vector diagram showing the magnetic field due to each of the two bottom wires and the total magnetic field at the location of the top wire. (1 pt)

b) Draw a vector representing the direction of the net force on the top wire due to the total magnetic field created by the bottom two wires. (1 pt)

c) If the bottom two wires both carry a current of 63.0 A, what is the magnitude of the total magnetic field at the location of the top wire? (3 pts)

d) The top wire is made of copper (density = 8.92 g/cm3) and has a radius of 1.00 mm. What is it’s mass per unit length in kg/m? (2 pts)

e) How much current must flow through the top wire so that the magnetic force on the top wire created by the currents in the bottom two wires is large enough to suspend the top wire? (3 pts)

Explanation / Answer

Here,

c)

From the geometry of the wires, the magnetic field vectors both are at an angle of 30 degree with the horizontal and that their y components cancel, so the resultant magnetic field:

B = (2*u0 *2* I*cos30 * i) / (4 *pie*R)

B = (2 * 10^-7 *2*63*cos30) / (0.075)

B = 0.00029098 T

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