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A solenoid of length 0.5 m has a radius of 1 cm and is made up of 250 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid?

Asked in GUJCET 2023 · Solenoid, toroid and field energy

• (1) 3.14×10⁻³ T
• (2) 6.28×10⁻³ T
• (3) 62.8×10⁻³ T
• (4) Zero

Step-by-step solution

Why the other options are wrong

• (2) 6.28×10⁻³ T is twice the answer: it is μ₀nI with n=1000 m⁻¹, which is what reading the length as 0.25 m gives. Here n=(250)/(0.5)=500 m⁻¹.
• (3) 62.8×10⁻³ T is that doubled value with the decimal point moved as well — two slips, not one. Sanity check: μ₀×500×5=3.14×10⁻³ T.
• (4) The field inside a solenoid is not zero: it is uniform and equal to μ₀nI. Zero is the field outside an ideal long solenoid, where the return flux spreads out.

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