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In a recent examination i encountered a question in which a current carrying coil was rotated clockwise about its own axis in a uniform magnetic field directed along the axis and out of the plane of the paper (refer the image provided below) and they asked the variation in tension in the wire.

currentinclosedloop

I know that if the loop had been at rest than the tension would have been T=BiR. But in the question provided as the loop had been rotating in the clockwise direction, so i thought that the apparent current (ie. the current that interacts with the magnetic field) will increase.Its like if the loop is rotating at 1rev/sec the the magnitude of our so called current will double and the tension will be equal to 2BiR.

However in the solution provided they mentioned that the tension will increase but it will be the result of the accelerated mass of the wire. here a clip of the solution

solutionclip

What the were trying to say was that the tension does not increase due to the apparent change in current magnitude neither does the tension depend on the direction of rotation.

Why so?

Any help is appreciated. Thank You

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Your intuition that there is an "apparent current" larger than the measured current is incorrect. It seems like your mental model of the coil is something like this: Current is a velocity of electrons around the coil. When the coil is stationary, those electrons are moving at some particular velocity around the ring. When the coil begins to rotate, that velocity increases -- and thus, so should the current.

This model is incorrect because it fails to account for the positive charges in the wire that keep it neutral. When the coil rotates, these positive charges also rotate with the coil, and this offsets the additional net velocity gained by the electrons that cause the measured current.

Put another way, your analysis would be on the right track if the coil were replaced by an electrically charged ring, since then rotating the ring leads to an increased charge flux through a cross section cutting through the ring. But since the coil is electrically neutral, rotating it doesn't have any effect on net charge flux anywhere.

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