Gauss law in Magnetism/Flux Figure is Described in Part 1 1. The figure below sh

Question

Gauss law in Magnetism/Flux

Figure is Described in Part 1

1. The figure below shows a straight current carrying conductor pointing straight up and two loops placed on either side. The loop on the left hand side of the conductor is a circle of radius r with velocity going upward. The loop on the right hand side is a rectangle with velocity going to the right.

2. The flux is defined as Flux=integral(B dot dA). If the radius of circular loop on the left is r then calculate the flux through the circular loop.

3. Calculate the flux through the rectangular loop shown on the right.

4. If the circular loop is moved with velocity v in the direction as shown in the figure then will the flux through the circular loop change? Assume the straight current carrying conductor is very long and the circular loop does not reach the end of the wire. Explain.

5. If the rectangular loop is moved to right with speed v, as shown in the figure, then will there be a change in magnetic flux through the loop. Explain.

Explanation / Answer

2. magnetic flux through circular loop phi = NAdB

where A is area = pi r^2

so

flux = pir ^2 B

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3. Magnetic flux throught rectangular loop is phi = NAB

area here for rectangle = ab

so magnetic flux = ab B

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Yes, change of field induces change of flux

this in turn creates inducec emf e = n. pi r^2. dB/dt

as such induced emf for a striaght conductor is given by e = lvB

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so as for recatngle

change of field induces change of flux

this in turn creates inducec emf e = n. ab . dB/dt

as such induced emf for a striaght conductor is given by e = lvB

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