COMEDK2021PhysicsMagnetic Effects of Current
A long solenoid has 20 turns cm ⁻¹ . The current necessary to produce a magnetic field of 20 mT inside the solenoid is approximately
Options
- A1 ~A
- B2 ~A
- C4 ~A
- D8 ~A
Correct answer
D. 8 ~A
Step-by-step solution
The magnetic field B inside a long solenoid is given by the formula B = ₀ n I , where n is the number of turns per unit length and I is the current. Given values are: B = 20 mT = 20 10⁻³ T n = 20 turns cm ⁻¹ = 20 10² turns m ⁻¹ = 2000 m ⁻¹ ₀ = 4 10⁻⁷ T m A ⁻¹ Substituting these values into the formula: 20 10⁻³ = (4 10⁻⁷) (2000) I 20 10⁻³ = 8 10⁻⁴ I I = 20 10⁻³ 8 10⁻⁴ = 200 8 = 25 Using 3.14 : I 25 3.14 7.96 A Rounding to the nearest integer, we get I 8 A . Answer: 8 ~A