Please answer BOTH parts. 1. Two wires carry current I 1 = 75 A and I 2 = 31 A i

Question

Please answer BOTH parts.

1. Two wires carry current I1 = 75 A and I2 = 31 A in the opposite directions parallel to the x-axis at y1 = 2 cm and y2 = 13 cm. Where on the y-axis (in cm) is the magnetic field zero?

2. You know you should not have bought the "MRI in a Box" kit from the Home Shopping Channel. Its main solenoid is supposed to have a radius of r=0.17 m, a length of L=0.26 m, and 14000 windings. The wire they give you has a resistance of 18 m? per meter. With only air inside, it's supposed to generate a field of 5.8 Tesla. What current would be needed?

Part B - How much power would your MRI device consume in steady operation?

Explanation / Answer

given,

I1 = 75 A

I2 = 31 A

y1 = 2 cm

y2 = 13 cm

let at distance be x where the magnetic field is 0

magnetic field due to wire = k * I / r

magnetic field due to I1 = 2 * 10^-7 * 75 / (x - 0.02)

magnetic field due to I2 = 2 * 10^-7 * 31 / (x - 0.13)

since both the magnetic field will be opposite in direction so,

2 * 10^-7 * 75 / (x - 0.02) - 2 * 10^-7 * 31 / (x - 0.13) = 0

x = 0.2075 m

magnetic field will be 0 at y = 20.75 cm

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