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The magnetic field Bin a certain region is 0.128 T, and its direction is that of the +z-axis in below figure (a) What is the magnetic flux across the surface in the figure? (b) What is the magnetic flux across the surface aefd? (c) What is the magnetic flux across the surface befc? (d) What the net flux through all five surface that enclose the shaded volume.

Short Answer

Expert verified

(a) The magnetic flux across the surface isfabcd=0Wb

(b) The magnetic flux across the surface is fbefc=-0.0115Wb.

(c) The magnetic flux across the surface is faefd=+0.0115Wb.

(d) The net flux through all five surface that enclose the shaded volume is 0Wb.

Step by step solution

01

Definition of magnetic flux

The term magnetic flux may be defined as the measurement of total magnetic field passing through the given area.

02

Determine the magnetic flux of surface area abcd and befc

The magnetic flux can be calculated as

From figure see that area vectors are perpendicular to the surface.

fabcd=B×Afabcd=BACos90fabcd=0

Hence, the magnetic flux across the surface isfabcd=0Wb

The area of the surface in the opposite direction of magnetic field so the magnetic flux calculated as

fbefo=B×Afbefo=BACos180fbeto=BAfbefc=B(be)(ef)

Here

be=0.300mef=0.300m

than

fbeft=(0.128T)(0.300m)(0.300m)fbeft=0.0115Wb

Hence, the magnetic flux across the surface is fbefc=-0.0115Wb.

03

Determine the magnetic flux of surface area and net flux

The angle between surface area and the magnetic field is

cos(θ)=30.050.0cos(θ)=35

Now the magnetic flux is

faetd=B×Afaefd=3BA5faefd=35(0.128T)(0.500m)(0.300m)faefd=+0.0115Wb

Hence, the magnetic flux across the surface aefd is faefd=+0.0115Wb.

And the net flux is zero because angle between them is90° .than

ftotal=fbefic+faefdftobl=0.0115Wb+0.0115Wbftotal=0

Hence, the net flux through all five surface that enclose the shaded volume is 0Wb.

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