Problem 4. A straight conductor carries a current 10.0A out of the page. Another

Question

Problem 4. A straight conductor carries a current 10.0A out of the page. Another straight conductor carries a current 12 15.0 A left to right in the plane of the page. The shortest distance between the conductors is (a) Determine the magnitude and direction of the net magnetic field at the point P that is midway be (b) Determine the magnitude and direction of the net magnetic field at the point Q that is 5.00 cm above (c) Determine the magnitude and direction of the net magnetic field at the point R that is 5.00 cm below 20.0cm. tween the conductors. 12.

Explanation / Answer

Given,

I1 = 10 A ; I2 = 15 a

a)Point P is at a distance of, d = 20/2 = 10 cm from both

Bnet-P = B1 - B2

Bnet = u0 I1/2 pi r1 - u0 I2/2 pi r2

Bnet-P = u0/2 pi [I1/r1 - I2/r2]

Bnet-P = 4 pi x 10^-7/2 pi [10/0.1 - 15/0.1] = -1 x 10^-5 T

Hence, Bnet-P = - 1 x 10^-5 T = -10 uT

b)d' = 5 cm

Bnet-Q = u0 I1/2 pi r1 - u0 I2/2 pi r2

Bnet-Q = u0/2 pi [I1/r1 - I2/r2]

r1 = 5 cm ; r2 = 25 cm

Bnet-Q = 4 pi x 10^-7/2 pi [10/0.05 - 15/0.25] = 2.8 x 10^-5 T

Hence, Bnet-Q = 2.8 x 10^-5 T = 28 uT

c)d'' = 5 cm

Bnet-R = u0 I1/2 pi r1 - u0 I2/2 pi r2

Bnet-R = u0/2 pi [I1/r1 - I2/r2]

r1 = 25 cm ; r2 = 5 cm

Bnet-R = 4 pi x 10^-7/2 pi [10/0.25 - 15/0.05] = -5.2 x 10^-5 T

Hence, Bnet-R = -5.2 x 10^-5 T = - 52 uT

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