NEETPhysicsElectromagnetic Induction
A conducting loop of resistance R is placed in a uniform, constant magnetic field B perpendicular to its plane. The area of the loop is continuously increased from an initial value A₀ at t=0 in such a way that the electrical power dissipated in the loop remains a constant value P₀ . Which of the following expressions represents the area of the loop as a function of time t ?
Options
- AA(t) = A₀ + P₀ R B^2 t^2
- BA(t) = A₀ + P₀ B R t
- CA(t) = A₀ e^ P₀ R B t
- DA(t) = A₀ + P₀ R B t
Correct answer
D. A(t) = A₀ + P₀ R B t
Step-by-step solution
The power dissipated in the loop is given by P = ^2 R , where is the induced EMF. Given that the power is a constant P₀ , we have: P₀ = ^2 R | | = P₀ R According to Faraday's law of electromagnetic induction, the magnitude of the induced EMF is: | | = | d dt | = B dA dt (since B is constant and perpendicular to the loop) Equating the two expressions for | | : B dA dt = P₀ R dA dt = P₀ R B Integrating with respect to time t , with the initial condition A(0) = A₀ : _ A₀ ^ A dA = ₀^ t P₀ R B dt A(t) - A₀ = P₀ R B t A(