A conducting square loop with edges of length 2.0 cm is rotated by 180^ around a diagonal in 0.20 s . A magnetic field B is present in the region, being perpendicular to the loop's initial position. Determine the magnitude of the magnetic field if the average induced emf during this rotation is 20 mV .

Step-by-step solution

The initial magnetic flux through the square loop is _ i = BA (0^ ) = BA . When the loop is rotated by 180^ around its diagonal, the final magnetic flux becomes _ f = BA (180^ ) = -BA . The magnitude of the change in magnetic flux is | | = | _ f - _ i | = |-2BA| = 2BA . The average induced emf is given by Faraday's law of induction: = | | t = 2BA t Given values are: = 20 mV = 20 10⁻³ V Side of the square loop, a = 2.0 cm = 2.0 10⁻² m Area of the loop, A = a^2 = (2.0 10⁻²)^2 = 4.0 10⁻⁴ m ^2 Time interval, t = 0.20 s