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Consider a circular loop of wire fixed on the rim of a wheel. This wire carries a current 'i' in it. When the wheel is at rest, which basically means that the current carrying loop is at rest, the magnitude of magnetic field at the center is, say B1. If I set the wheel in motion with a constant angular velocity with the center of the wheel at rest and without changing the current in the loop, which implies that the current carrying loop rotates about its center point, will the magnitude of magnetic field change at the center point?

I think that it will change because number of charges passing through a unit cross section which is at relative rest with respect to the center point changes and hence current effectively changes and hence magnetic field changes. Is this correct?

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  • $\begingroup$ Is the magnetic field due to charges or is it applied if it is due to current carrying loop then we see that initially also the loop Carrie's a current and finally also it is carrying a current . The affect of rotation in frame of wheel will cancel out as both the centre and rim have acquired w . Kindly confirm which field are you talking about $\endgroup$
    – Anusha
    Oct 12 '20 at 11:26
  • $\begingroup$ The magnetic field is due to the charges moving inside the conductor. $\endgroup$ Oct 12 '20 at 11:51
  • $\begingroup$ @anusha I think "bicycle" wheel made this a bit unclear. It's just a current carrying loop rotating around it's center with the center at rest. Will the magnetic field change ? $\endgroup$ Oct 12 '20 at 11:55
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I'm thinking that with the wheel rotating, the motion of the positive charges will constitute an electric current that offsets the change in the motion of the free electrons.

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  • $\begingroup$ I agree with you. As their are equal number of positive charges to keep the wire electrically neutral, their field counters the field generated by negative charges $\endgroup$ Oct 13 '20 at 1:50
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The situation resembles alot to a rotating loop. So I'm using this as a hint .The formula for calculating magnetic field at the centre of a current carrying loop is directly proportional to i/R. We see that when the ring rotates the current in a small area remains constant.


This is because when the loop rotates the part of loop which crosses a region and the part which enters that region remains same . Considering that the current is constant the magnetic field has to remain constant

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  • $\begingroup$ I don’t think that’s what’s happening here. The “current” does remain constant but the rate at which charges pass through a given cross section perpendicular to their direction of propagation in the wire increases or simply their speed increases. But, the magnetic field remains constant as positive charges acquire the same angular velocity and nullify the effect of negative charges as suggested by @R.W.Bird $\endgroup$ Oct 13 '20 at 1:40
  • $\begingroup$ How do the charges increase if the current is constant $\endgroup$
    – Anusha
    Oct 13 '20 at 3:46
  • $\begingroup$ who said that the charges increase? We are talking about the rate at which they pass through a given cross section or in simple words their speed $\endgroup$ Oct 13 '20 at 5:18

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