Two long, parallel transmission lines, 50.0 cm apart, carry 20.5-A and 73.5-A cu

ID: 1373552 • Letter: T

Question

Two long, parallel transmission lines, 50.0 cm apart, carry 20.5-A and 73.5-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 73.5 A and_________m from the wire carrying current 20.5 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 20.5 A and_________m from the wire carrying current 73.5 A.

apply magnetic field B = uoi /2piR in each case

so here let field be zero at x units from 20.5 A wire, or this is at distance of

(0.5-x) from 73.5 A

as B1 = B2

uoi1/2pix = uoi2/(2pi(0.5-x)

20.5/x = 73.5/(0.5-x)

0.5-x/x = 73.5/20.5

0.5-x = 3.58 x

4.58 x= 0.5

x = 0.5/4.58

x = 11cm from 20.5 A wire net field is Zero

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let field be zero at x units from 73.5 A

or at (0.5 + x) from 20.5 A

so 20.5/(X+0.5) = 73.5/x

20.5 x = 73.5x + 36.75

x = 36.75/(20.5-73.5)

x = 69.33 cm from 73.5 A

or 119.33 cm from 20.5 A wire

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