A non conducting ring of radius r has a charge Q uniformily distriubuted over it. a magnetic field perpendicular to the plane of the ring changes at the rate dB/dT. the torque experienced by the ring = ?? . will there be any difference if the ring is conducting?whyor why not?

Question

A non conducting ring of radius r has a charge Q uniformily distriubuted over it. a magnetic field perpendicular to the plane of the ring changes at the rate dB/dT. the torque experienced by the ring = ?? . will there be any difference if the ring is conducting?whyor why not?

AJIT AskiitiansExpert-IITD · Answer

Dear golu ,

Case I : Apply following equation - ∫_lineE.dl = - dØ/dt i.e line integral of electric field over a surface is the rate change of flux through that surface. note that bold letters are vectors.

now , varying magnetic field produces electric field , direction given by right hand thumb rule. we can see that electric field is in circular direction along the ring , assume it to be E (magnitude) . it will be constant as ring is symmetrical.

Therefore , E.2∏r = ∏r² * dB/dt ; E = (1/2)*dB/dt. now we can easily see torque = EQr = (1/2)*dB/dt*Qr.

Case II: in first case there was no conduction so ring moved with charges but in this case charges shall move inside the ring because ring allows conduction . so a current will flow and ther will not b any torque on ring.

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A non conducting ring of radius r has a charge Q uniformily distriubuted over it. a magnetic field perpendicular to the plane of the ring changes at the rate dB/dT. the torque experienced by the ring = ?? . will there be any difference if the ring is conducting?whyor why not?

A non conducting ring of radius r has a charge Q uniformily distriubuted over it. a magnetic field perpendicular to the plane of the ring changes at the rate dB/dT. the torque experienced by the ring = ?? . will there be any difference if the ring is conducting?whyor why not?