A rod of mass m can rotate without friction about axis sliding (also without friction) along a conducting ring of radius b arranged in a vertical plane as shown in the . The entire arrengement is placed in a uniform magnetic field with the inducetion B perpendicular to the plane of the ring. The axis and the conductor are connected to teh terminals of a current source. Determine (a) according to which law current I flowing in the rod must vary for the rod to rotate at a constant angular speed. Being to measure the time from the instant when the rod is in its right-hand horizontal position. Consider the current to be positive when it flows from the axis of rotation toward the ring. (b) what emf E of the source must be applied to maintain the required current? Consider the total resistance of the circuit to be constant and equal to R. Disergard the inductance of teh circuit.

A rod of mass m can rotate without friction about axis sliding (also w

1.	A rod of mass m can rotate without friction about axis sliding (also without friction) along a conducting ring of radius b arranged in a vertical plane as shown in the . The entire arrengement is placed in a uniform magnetic field with the inducetion B perpendicular to the plane of the ring. The axis and the conductor are connected to teh terminals of a current source. Determine (a) according to which law current I flowing in the rod must vary for the rod to rotate at a constant angular speed. Being to measure the time from the instant when the rod is in its right-hand horizontal position. Consider the current to be positive when it flows from the axis of rotation toward the ring. (b) what emf E of the source must be applied to maintain the required current? Consider the total resistance of the circuit to be constant and equal to R. Disergard the inductance of teh circuit.
Answer» SOLUTION :(a) `tau_(B) = F_(B) xx (b)/(2)rarr tau_(B) = IbB xx (b)/(2) = IB(b^(2))/(2)` `tau_(net) = 0 `rarr` MG COS THETA xx (b)/(2) = (IBb^(2))/(2)` `rarr` `mg cos theta = IBb` `theta = omegat` `rarr` `I = (mg cos omegat)/(Bb)` (b) `((E - E_(i nd)))/(R) = I`, `E = E_(i nd). + IR` `rarr` `E = (Bomegab^(2))/(2) + (mg R cos omegat)/(Bb)`

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