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# Answer to Question #121649 in Mechanics | Relativity for nicolee heath

Question #121649
A square conducting loop of side L contains a resistor, R. It is placed in a magnetic field, B, directed into the page and which changes as a function of time t according to the relationship B = at + b, where a and b are positive constants. No magnetic field exists outside the loop.

Derive an expression for the induced current in the loop in terms of a, b, L, and/or R (note: not all terms may be in your final expression).
Derive a similar expression in terms of a, b, L, and/or R for the power dissipated in the resistor.
Does the induced current flow clockwise or anticlockwise? Explain.
The square loop is replaced by a circular copper loop of diameter 0.20 m and consisting of 50 turns. If a = 10 and b = 2, determine the emf induced in the circular loop.
1
2020-06-11T10:34:45-0400

"Solution.\\\\1)\\;the\\; area\\; of\\; a\\; square\\;S=L^2\\\\i=-\\frac{S}{R}\\times\\frac{dB}{dt};\\\\i=-\\frac{L^2}{R}\\times a ;\\\\2)\\;the \\;current\\; is \\;constant, so\\\\P=I^2R\\;orP=a^2R\\\\3)\\;The \\;current\\; flows\\; counter\\;clockwise.\\\\the\\; induction\\; current\\; creates \\\\a\\; field\\; directed \\;against\\; the\\; external\\; field.\\\\4)E_i=-S\\times\\frac{dB}{dt}\\times n;\\\\E_i=-\\frac{\\pi\\times d^2}{4}\\times\\frac{dB}{dt}\\times n;\\\\E_i=-0.0314\\times 10\\times 50=15.7V"

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