The magnetic flux through a stationary loop of wire having a resistance R varies with time as =4 t^2+3 t . The average emf and total charge flowing in the loop in the time interval t=0 to t= respectively are

Step-by-step solution

The magnetic flux is given by (t) = 4t^2 + 3t . The average induced emf _ avg in the time interval t=0 to t= is defined as the change in flux divided by the time interval: _ avg = - t = - ( ) - (0) - 0 Substituting the values: ( ) = 4 ^2 + 3 (0) = 4(0)^2 + 3(0) = 0 _ avg = (4 ^2 + 3 ) - 0 = (4 + 3) = 4 + 3 The total charge q flowing through the loop is given by q = R , where is the magnitude of the change in flux: q = | ( ) - (0)| R = 4 ^2 + 3 R Answer: 4 +3, 4 ^2+3 R