Give the formula\'s for both a & b. In the figure below, a rectangular loop of w

Question

Give the formula's for both a & b. In the figure below, a rectangular loop of wire with length a, width b, and resistance R is placed near an infinitely long wire carrying current i. The loop is then moved away from the wire at constant speed v. (Use any variable or symbol stated above along with the following as necessary: ?0, where all quantities are in SI units.) (a) When the center of the loop is at distance r, find the magnitude of the magnetic flux through the loop. (b) Find the current in the loop at distance r.

Explanation / Answer

B at distance r from wire is mu0 i/(2 pi r) flux = int [B.da] = int [mu0 i / (2pi x) a dx] from r - b/2 to r+b/2 flux = mu0 i a/2pi (ln(r + b/2) - ln(r - b/2)) current in loop I' is EMF/R EMF = - rate of change of flux I' = mu0 i a (b/(r^2 - b^2/4)) v/(2pi R) as we move away from the coil the flux reduces hence the current set up will oppose this change hence current will flow clockwise! if loop moves horizontally there will be no change in flux...since dr/dt = 0 d flux/dt = 0 EMF = 0 I' = 0

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