A conducting circular loop is placed in X - Y plane in presence of magnetic field B → = 3 t 3 j ^ + 3 t 2 k ^ in SI unit. If the radius of the loop is 1 m , the induced emf in the loop, at time, t = 2 s is n π V . The value of n is _____ .

Step-by-step solution

By the faraday's law in electromagnetic induction ε i n d = - d ϕ d t = - d B → · A → d t Magnetic flux is ϕ = B → · A → = 3 t 3 j ^ + 3 t 2 k ^ · π 1 2 k ^ So, ϕ = 3 t 2 π Now, induced emf is ε i n d = d ϕ d t = 6 t π At t = 2 ,   ε i n d = 6 2 π = 12 π   V . Thus, the value of n = 12 .