# The Red Conducting Carpet.

Electricity and Magnetism Level 4

A red carpet surprisingly found conducting has resistance $$m$$ and total mass $$M$$ and when rolled completely has radius $$R.$$ With a gentle negligible push it starts rolling on the ground with a velocity of $$v$$ and radius $$r.$$ There exists a uniform magnetic field perpendicular to the base of the carpet the whole time. Let the whole motion stop after a time $$T.$$ The rms value of $$vr$$ during this time interval from $$t=0$$ to $$t=T$$ is $$n.$$ The centre is connected to the other end by a long wire of negligible resistance. Neglect any strain in the carpet. Then what is the value of $$[(n^2)/4]?$$

Details and Assumptions

• $$T=10\text{ sec}$$
• $$R=5\text{ m}$$
• $$M=2\text{ kg}$$
• $$m=30\ \Omega$$
• $$g=9.8\text{ m/s}^{2}$$
• $$B=\pi\text{ T}$$
• [.] denotes the greatest integer function
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