A conducting circular loop is placed in a uniform magnetic field with its plane perpendicular to the field. The radius of the loop is shrinking at a constant rate of 2 mm s ⁻¹ . At the instant when the radius of the loop is 5 cm , the magnitude of the induced emf in the loop is 10 V . The magnitude of the uniform magnetic field is _______ mT .

Step-by-step solution

According to Faraday's law of induction, the magnitude of the induced emf is given by: = | d dt | The magnetic flux through the circular loop is = B A = B r^2 . Since the magnetic field is constant, the rate of change of flux is: = B d dt ( r^2) = B 2 r | dr dt | Given data: = 10 V = 10 10⁻⁶ V r = 5 cm = 0.05 m | dr dt | = 2 mm s ⁻¹ = 0.002 m s ⁻¹ Substituting these values into the equation: 10 10⁻⁶ = B 2 (0.05) (0.002) 10 10⁻⁶ = B 2 10⁻⁴ Solving for B : B = 10 10⁻⁶ 2 10⁻⁴ = 5 10⁻² T Converting to milliTesla (mT):