cylindrical volume of radius R has a uniform axial magnetic field B, which is increasing at a rate of `(dB)/(Dt) = alpha Ts^(-1)`. A chord (AB) of the circular cross section of the cylindrical region has length L.Calculate the line integral of induced electric field `(int_(A)^(B) vec(E) vec(dl))` as one moves along the chord from A to B. Try to find the answer without actually performing the integration. Is the value of integral same if one moves along the arc from A to B ?

cylindrical volume of radius R has a uniform axial magnetic field B, w

1.	cylindrical volume of radius R has a uniform axial magnetic field B, which is increasing at a rate of `(dB)/(Dt) = alpha Ts^(-1)`. A chord (AB) of the circular cross section of the cylindrical region has length L.Calculate the line integral of induced electric field `(int_(A)^(B) vec(E) vec(dl))` as one moves along the chord from A to B. Try to find the answer without actually performing the integration. Is the value of integral same if one moves along the arc from A to B ?
Answer» Correct Answer - `(L alpha)/(4) sqrt(4R^(2)-L^(2))`

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