Two long, parallel transmission lines, 39.0 cm apart, carry 30.0-A and 74.0-A cu

Question

Two long, parallel transmission lines, 39.0 cm apart, carry 30.0-A and 74.0-A currents.

(a) Find all locations where the net magnetic field of the two wires is zero if the currents are in the same direction.

Btot = 0 along a line _____ m from the wire carrying 74.0 A and ______ m from the wire carrying current 30.0 A.

(b) Find all locations where the net magnetic field of the two wires is zero if the currents are in the opposite direction.

Btot = 0 along a line_________ m from the wire carrying 30.0 A and ______ m from the wire carrying current 74.0 A.

Explanation / Answer

a)

here

If current are in the same direction then the null point has to lie within the two wires.
Let x be the distance of the point from 30A conductor. Then the point is at (0.39 - x) right from 74A conductor
So as they have to be equal in magnitude,

so ,

30/x = 74 / (0.39 - x)

30 * 0.39 - 30x = 74x

x = 0.11m
Btot = 0 along a line 0.28 m from the wire carrying 74.0 A and 0.11 m from the wire carrying current 30.0 A

b)

Now if current flows in opposite direction then null points could be outside on both sides.'

So it is at x1 right from 25A conductor side.

25 / x1 = 75 / (0.39 + x1)

x1 = 11.7 / 44

x1 = 0.26 m
Btot = 0 along a line 0.26 m from the wire carrying 30.0 A and 0.65 m from the wire carrying current 74.0 A

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.