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In the given figure, two circles with ce...

In the given figure, two circles with centres A and B touch each other at C bisects the common tangent at P and Q.

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1. Here point O is on the line of horizontal currents, hence the magnetic field is not developed due to them. It also lies on the directions of radial currents hence magnetic fields due to them is also zero. So the magnetic field is produced only due to the arc. To find this, the formula of magnetic field at the center of a ring having n turns and radius R can be used. According to this equation,
`B=(mu_(0)nI)/(2R)` (in a direction going into the plane of paper) ....(1)
2. In the present case, the length of the arc is R`theta` For one complete turn, the length of the arc is `2piR`, then the number of turns for length R`theta` will be,
`2piR:1` turn
`Rtheta:?rArr` number of turns, `n=(Rtheta)/(2piR)=theta/(2pi)` Using this in equation (1),
`B=(mu_(0)Itheta)/(2Rxx2pi)`
`thereforeB=(mu_(0)Itheta)/(4piR)` (going into the plane of figure)
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