Practice portal › Moving Charges and Magnetism › Ampere's Circuital Law, Solenoid and Toroid

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 1000 turns. It carries a current of 10 A. What is the magnitude of the magnetic field inside the solenoid?

Asked in GUJCET 2021 · Solenoid, toroid and field energy

• (1) 6.28×10⁻³ T
• (2) 2.51×10⁻² T
• (3) 1.71×10⁻² T
• (4) 7.23×10⁻³ T

Step-by-step solution

Why the other options are wrong

• (1) 6.28×10⁻³ T comes from multiplying by the length instead of dividing: 1000×0.5=500 used as the turn density gives μ₀×500×10=6.28×10⁻³ T. The turn density is (1000)/(0.5)=2000 per metre.
• (3) No single slip gives 1.71×10⁻² T. Sanity check: n=2000 m⁻¹ and I=10 A fix B=μ₀nI=8π×10⁻³=2.51×10⁻² T.
• (4) 7.23×10⁻³ T is not reachable either. With μ₀=4π×10⁻⁷ the answer is a multiple of π, here 8π×10⁻³ T; the 1 cm radius is a red herring, as the field inside a long solenoid does not depend on it.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.