Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2019PhysicsElectromagnetic InductionActual

A semicircular wire of radius r rotates in uniform magnetic field B about its diameter with angular velocity ω . If the total resistance of the circuit is R , then the mean power generated per period of rotation is

Options

  1. Aπ B r 2 ω 2 8   R
  2. Bπ B r ω 2 8 R
  3. Cπ B r ω 2 8   R
  4. D0

Correct answer

A. π B r 2 ω 2 8   R

Step-by-step solution

The flux linked with coil (made of wire of radius r ) of area A and magnetic field B , is given by ϕ = B A   cos   θ = B   π r 2 2   cos   ω t ϕ = π B r 2 2   cos   ω t [ ∵         A = π r 2 2 and θ = ω t ] By Faraday's law of electromagnetic induction, induced emf, e = - d ϕ d t Hence, after differentiating, e = - d d t π B r 2 2   cos   ω t = π B r 2 ω 2   sin

Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

Inside a solenoid of radius 0.5 m , magnetic field is changing at a rate of 50 10⁻⁶ ~T / s . Acceleration of an electron placed at a distance of 0.3 m from axis of solenoid will be 2024There are two long co-axial solenoids of same length l . The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂ , respectively. The ratio of m 2024A rectangular loop of length 2.5 m and width 2 m is placed at 60^ to a magnetic field of 4 T . The loop is removed from the field in 10 sec . The average emf induced in the loop du 2024A 12 ~V battery connected to a coil of resistance 6 through a switch, drives a constant current in the circuit. The switch is opened in 1 ~ms . The emf induced across the coil is 2 2023In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial reson 2023A conducting loop of radius 10 cm is placed perpendicular to a uniform magnetic field of 0.5 T . The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf 2023A metal disc of radius 100 ~cm is rotated at a constant angular speed of 60 rad / s in a plane at right angles to an external field of magnetic induction 0.05 ~Wb / m ² . The emf i 2021A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction B constant in time and space 2020 Full Electromagnetic Induction list All BITSAT PYQs