Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
A long solenoid is constructed by tightly winding a wire of radius 0.5 mm around a cylindrical nonmagnetic frame, ensuring that successive turns nearly touch one another. If the solenoid carries a current of 5 A , determine the magnetic field B at its centre.
Options
- A2 10⁻³ T
- B2 10⁻³ T
- C10⁻³ T
- D4 10⁻³ T
Correct answer
B. 2 10⁻³ T
Step-by-step solution
The magnetic field at the centre of a long solenoid is given by B = ₀ n I , where n is the number of turns per unit length. Since the wire is tightly wound, the distance between successive turns is equal to the diameter of the wire. Diameter of the wire d = 2r = 2 0.5 mm = 1 mm = 10⁻³ m . The number of turns per unit length is n = 1 d = 1 10⁻³ = 1000 m ⁻¹ . Substituting the values in the formula for magnetic field: B = 4 10⁻⁷ 1000 5 B = 20 10⁻⁴ T = 2 10⁻³ T .