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A circular area with a radius of6.50cmlies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic fieldlocalid="1655727900569" B=0.230T(a) in the direction of +z direction; (b) at an angle of53.1°from the direction; (c) in the direction?

Short Answer

Expert verified

(a) The magnitude of the magnetic flux is3.05×10-3T.m2through this circle due to a uniform magnetic fieldB=0.230Tin the direction of +Zdirection.

(b)The magnitude of the magnetic flux is1.83×10-3T.m3through this circle due to a uniform magnetic field B=0.230Tat an angle of from the +Zdirection.

(c) The magnitude of the magnetic flux is zero through this circle due to a uniform magnetic fieldB=0.230Tin the +Zdirection.

Step by step solution

01

Definition of flux

The term flux may be defined as the specified physical medium having presence of force field

02

Determine magnitude of the magnetic flux in direction

The magnetic flux can be calculated as


fB=B×dAfB=BdAcosθfB=BAcos0fB=BAfB=πR2B

Here R is the radius of circle and B is the magnetic field.

Substitute all the value in the above equation.

fB=π6.50×10-2m20.230TfB=3.05-3T.m2

Hence, the magnitude of the magnetic flux is3.05-3T.m2through this circle due to a uniform magnetic field B=0.230T/in the direction of direction.

03

Determine magnitude of the magnetic flux at an angle of from the direction.

The magnetic flux can be calculated as

fB=B×dAfB=BdAcosθfB=BAcos53.1°fB=πR2cos53.1°

Here R is the radius of circle and B is the magnetic field.

Substitute all the value in the above equation.

fB=π6.50×10-2m0.250Tcos53.1°fB=1.83×10-3T.m2

Hence, the magnitude of the magnetic flux is1.83×10-3T.m2 through this circle due to a uniform magnetic fieldB=0.230T at an angle of 53.1°from the+y direction.

04

Determine the magnitude of the magnetic flux in the+ydirection

The magnetic flux can be calculated as


fB=B×dAfB=BdAcosθfB=BAcos90°fB=0

Hence, the magnitude of the magnetic flux is zero through this circle due to a uniform magnetic fieldB=0.230Tin the +ydirection.

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