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Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry respectively 0.2 A and 0.3 A currents in opposite direction. The magnetic field in tesla at the centre is
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
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Given Information:
- Two concentric circular coils with 10 turns each
- Radii of the coils are 20 cm and 40 cm
- Current in the first coil = 0.2 A
- Current in the second coil = 0.3 A
- Currents flow in opposite directions
Formula for Magnetic Field at the Centre of a Circular Coil:
The formula for the magnetic field at the center of a circular coil is given by:
\[ B = \frac{{\mu \cdot N \cdot I}}{2r} \]
Where,
- B is the magnetic field
- μ is the permeability of free space (4π x 10^-7 Tm/A)
- N is the number of turns in the coil
- I is the current flowing through the coil
- r is the radius of the coil
Calculation:
1. For the first coil with a radius of 20 cm:
\[ B_1 = \frac{{4\pi \times 10^{-7} \cdot 10 \cdot 0.2}}{2 \times 0.2} \]
\[ B_1 = \frac{{8\pi \times 10^{-6}}}{0.4} \]
\[ B_1 = 20\pi \times 10^{-6} \]
2. For the second coil with a radius of 40 cm:
\[ B_2 = \frac{{4\pi \times 10^{-7} \cdot 10 \cdot 0.3}}{2 \times 0.4} \]
\[ B_2 = \frac{{12\pi \times 10^{-6}}}{0.8} \]
\[ B_2 = 15\pi \times 10^{-6} \]
3. Since the currents flow in opposite directions, the net magnetic field at the center is:
\[ B = B_2 - B_1 \]
\[ B = 15\pi \times 10^{-6} - 20\pi \times 10^{-6} \]
\[ B = -5\pi \times 10^{-6} = -5 \times 4\pi \times 10^{-7} = -5 \times \mu \]
Therefore, the magnetic field at the center of the coils is \( 5\mu \) T in the opposite direction. Hence, the correct answer is option 'D'.
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Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry respectively 0.2 A and 0.3 A currents in opposite direction. The magnetic field in tesla at the centre isa) 35 μ 0 ∕ 4 b) μ 0 ∕ 80 c) 7 μ 0 ∕ 80 d) 5 μ 0 ∕ 4 Correct answer is option 'D'. Can you explain this answer?
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