Question

A rectangular coil of wire with an area of 0.167 m² is situated in a constant magnetic field whose magnitude is 0.406 T. Suppose the normal to the surface of the coil is parallel to the direction of the magnetic field (this means the magnetic field is also normal, or perpendicular, to the surface of the coil). What is the flux through the surface?

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If the area of the coil is reduced to 0.110 m² while keeping the orientation of the coil the same, what is the new flux through the surface?

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Go back to a coil with an area of 0.167 m², but instead rotate the coil such that the normal to the surface of the coil is perpendicular to the direction of the magnetic field (this means the magnetic field is parallel to the surface of the coil). What is the flux through the surface?

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Answer 1

a)

From given data,

i) Magnitude of magnetic field is

ii) Cross-sectional area of wire is

iii) Given orientation of magnetic filed to surface of coil is

Magnetic flux is given by the product of component of magnetic field perpendicular to surafce of coil and cross-sectional area.

Thus, magnetic flux is

  

Substitute all the known values,

  

  

Thus, the magnetic flux is

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b)

From given data,

i) Magnitude of magnetic field is

ii) Cross-sectional area of wire is

iii) Given orientation of magnetic filed to surface of coil is

Thus, magnetic flux is

  

Substitute all the known values,

  

  

Thus, the magnetic flux is

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c)

From given data,

i) Magnitude of magnetic field is

ii) Cross-sectional area of wire is

iii) Given orientation of magnetic filed to surface of coil is

Thus, magnetic flux is

  

Substitute all the known values,

  

  

Thus, the magnetic flux is