Two circular loops of wire lie in the x-y plane, centered at the origin. The radius of the loops is 5.00 and 7.00 cm. The current in the outer loop is 50.0 mA in the clockwise direction.a. If the current in the inner wire is also 50.0 mA in the clockwise direction, what is the magnetic field strength at the origin?b. What current magnitude and direction in the inner wire will cause the magnetic field to be zero at the origin?

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Asked Oct 23, 2019
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Two circular loops of wire lie in the x-y plane, centered at the origin. The radius of the loops is 5.00 and 7.00 cm. The current in the outer loop is 50.0 mA in the clockwise direction.

a. If the current in the inner wire is also 50.0 mA in the clockwise direction, what is the magnetic field strength at the origin?

b. What current magnitude and direction in the inner wire will cause the magnetic field to be zero at the origin?

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Expert Answer

Step 1

Consider the radius of the outer loop be Ro, the radius of the inner loop be Ri, the current flow in the outer loop be Io, the current flow in the inner loop be Ii, the magnetic field strength due to the current Io be Bo, and the magnetic field strength due to current Ii be Bi, and the net magnetic field strength be B.

 

The given values are,

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1A I 50.0 mA = 50.0 mA -0.05 A 1000 mA 1m R 7.0 cm 7.0 cm =0.07 m 100 cm 1 m R 5.0 cm 5.0 cm =0.05 m 100 cm

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Step 2

(a)

 

Since, the currents flow in the both loops in clockwise direction, from the Right-hand rule, the direction of the net magnetic field will be into the page.

 

The magnitude of the net magnetic field strength can be calculated as,

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B B+B = 2R, 2R I 2 R, R 47T x107 T m/A(0.05 A 0.05 A' 0.05 m 0.07 m 2 1.077x106 T

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Step 3

(b)

 

Write the expression for the magnitude of the net magnetic field strength, that is, zero...

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B- B+B 2R, 2R 0 = 2R, 2R 2R 2R, (0.05 m)(0.05 A) RI 0.07 m (1000 mA I-0.0357 A :-35.7 mA 1 A

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