a piece of copper wire is formed into a rectangle. The length of the rectangle i

Question

a piece of copper wire is formed into a rectangle. The length of the rectangle is 3m and the width is 2m. A magnetic field is everywhere oriented parallel to the normal to the loop(into the drawing), and it increases from 1T to 2Teslas in a time of 2 seconds. The wire has a resistance per unit length of (1/10) ohms/meter. what is the average electrical energy dissipated in the resistance of the wire?? The answer is 18J. How do I get that??

Explanation / Answer

? area of circular loop : A = 6m^2 ? change in magnetic field : ?B = 1 Tesla . . . . . . . . . . . . . . . . . . . . . . . . ?B = 1 Tesla ? (in a time : ?t = 2 s) ? resistance per unit length = .1 O/m ? total resistance : R = .1*13 = 1.3O/m ? induction voltage from change in magnetic field : => V = N (?F/?t) . . . . . . (N = the number of turns ? N = 1) => V = (?B A) / (?t) => V = A (?B / ?t) => V = 6 (1 / 2) => V =3volt ? the average electrical energy dissipated (per unit time) : => P = E/t = (V²/R) => P = 9 / 1.3 => P =6.92Joule/seconds ? energy dissipated for t = 0.45 s : => E = P t => E = (0.15319) (0.45) => E = 0.069 Joule

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