Answer to Question #282929 in Electricity and Magnetism for BIGIRMANA Elie

Question

 A rectangular loop of conducting wire with sides 3.0 m and 1.0 m is perpendicular to a uniform magnetic field The magnitude of the magnetic field varies with time as B = 0.08 + 0.75 t, where B is in Teslas and t is in seconds. A battery of 12.0V and negligible resistance is connected in the loop as shown in the figure. (a) Determine the total emf in the circuit. (b) What is the direction of the current through the circuit? 19. What inductance will be needed to store 1.00 Wh of energy in a coil carrying a current of 20 A?

Answer 1

$\varepsilon=U+\frac{d\Phi}{dt}=U+S\frac{dB}{dt}=U+ab\frac{dB}{dt}=12+3\cdot 1\cdot0.75=14.25~V,$

$W=\frac{LI^2}2,\implies L=\frac{2W}{I^2}=\frac{2\cdot 1\cdot3600}{20^2}=18~H.$