Electro Magnetic Induction And Alternating Currents Question 515

Question: A nonconducting ring of mass m and radius R has a charge Q uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that the plane of the ring is parallel to the surface. A vertical magnetic field B=B0t2 tesla is switched on. After 2 second from switching on the magnetic field the ring is just about to rotate about vertical axis through its centre. Then

Options:

A) the induced electric field is quadratic in time t

B) the force tangential to the ring is 9B0QRt

C) until 2 seconds, the friction force does not come into play

D) the friction coefficient between the ring and the surface is 2B0RQmg .

Show Answer

Answer:

Correct Answer: D

Solution:

  • Magnitude of induced electric field due to change in magnetic flux is given by

    E,.d,=dϕdt=AdBdt (N=1,and,cos,θ=1)

    or E.=πR2(2B0t) (dBdt=2B0t)

    Here, E = induced electric field due to change in magnetic flux

    E(2πR)=2πR2B0t or E=B0Rt

    Hence, F=QE=B0QRt This force is tangential to ring.

    Ring starts rotating when torque of this force is greater than the torque due to maximum friction (fmax=μmg) or when τFτfmax

    Taking the limiting case, τF=τfmax

    or F.R=(μmg)R

    It is given that ring starts rotating after 2 seconds So, putting t=2 seconds,

    we get μ=2B0RQmg



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