Q1 (2024)
A 100-turn closely wound circular coil of radius $5\mathrm{cm}$ has a magnetic field $3.14\times 10^{-3}\mathrm{T}$ at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of the coil are, respectively - (Take $\mu_0 = 4\pi \times 10^{-7}\mathrm{Tm / A})$
- $2.5\mathrm{A}, 2\mathrm{Am}^2$
- $2.5\mathrm{A}, 20\mathrm{Am}^2$
- $2\mathrm{A}, 4\mathrm{Am}^2$
- $2\mathrm{A}, 10\mathrm{Am}^2$
### Related Formula
$$B_{0} = \frac{\mu_{0}Ni}{2R}$$
$$M = NiA = Ni(\pi R^2)$$
### Core Logic
Step 1: Calculate current $i$:
$$i = \frac{2RB_{0}}{\mu_{0}N} = \frac{2\times 5\times 10^{-2}\times 3.14\times 10^{-3}}{4\pi\times 10^{-7}\times 100} = 2.5\mathrm{A}$$
Step 2: Calculate magnetic moment $M$:
$$M = NiA = 100\times 2.5\times 3.14\times \left(5\times 10^{-2}\right)^{2} = 2\mathrm{Am}^{2}$$
### Pattern Recognition
Standard formula application for circular coil central magnetic field and magnetic dipole moment.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Magnetic Effects of Current and Magnetism
