If a uniform B field is perpendicular to an area A, then If B field is not perpe

ID: 1609803 • Letter: I

Question

If a uniform B field is perpendicular to an area A, then

If B field is not perpendicular to an area A but at an angle to the normal n, then

Total flux thru A = = BA cos = (B.n)A

The unit of flux is Weber (Wb). Now solve this problem.

A circular area of radius 4 cm lies on the xy plane.

a) What is the flux thru this circle if the uniform field is B = 5.5 k T?

b) What is the flux thru this circle if the uniform field is B = (2 i + 5.5 k )T

c) What is the flux thru this circle if the uniform field is B = ( i + 3 j + 5.5 k )T?

(Hint: Use the relationships i.k = j.k = i.j = 0, i.i = j.j = k.k = 1.)

dA Area A

here Area A = pi*r^2 = pi*0.04^2 = 0.005026 m^2

here unit vector n is perpendicular plane xy, thus n = k

a) magnetic flux = (B.n)A

phi B = (5.5k.k)*0.005026 = 5.5*0.005026 = 0.027643 Wb

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(b) magnetci flux = (B.n)A = (2i + 5.5k).k)*0.005026

phiB = 0 + 5.5*0.005026

phi B = 0.027643 Wb

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(c) flux = (B.n)A

phi B = (i + j + 5.5k).k)*0.005026

phi B = 0 + 0 + 5.5*0.005026

phi B = 0.027643 Wb

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