COMEDK2025PhysicsMagnetic Effects of CurrentActual
A long solenoid X having 400 turns per cm carries a current I . The magnetic field produced at its centre by this solenoid is 3.14 10⁻² T . The magnetic field produced by another solenoid Y at its centre having 300 turns per cm carries a current I 3 . The magnetic field produced by Y at its centre is:
Options
- A12.56 10⁻² T
- B0.785 10⁻² T
- C1.256 10⁻² T
- D2.785 10⁻² T
Correct answer
B. 0.785 10⁻² T
Step-by-step solution
The magnetic field B at the centre of 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. For solenoid X, we have n_ X = 400 turns/cm = 40000 turns/m and B_ X = 3.14 10⁻² T . For solenoid Y, we have n_ Y = 300 turns/cm = 30000 turns/m and current I_ Y = I 3 . Taking the ratio of the magnetic fields: B_ Y B_ X = ₀ n_ Y I_ Y ₀ n_ X I_ X = n_ Y n_ X I_ Y I_ X Substituting the values: B_ Y 3.14 10⁻² = 300 400 I/3 I = 3 4 1 3 = 1 4 B_ Y = 3.14 10⁻² 4 T