A circular coil of wire consisting of 500 turns, each of radius 6.0 cm carries a current of 0.30 A. Find the magnitude of the magnetic field B at the center of the coil?

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  1. 5.0 × 10-4 T
  2. 3.14 × 10-4 T
  3. 1.57 × 10-3 T
  4. 5.0 × 10-3 T

Answer (Detailed Solution Below)

Option 3 : 1.57 × 10-3 T
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Detailed Solution

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Concept:

Using the formula for the magnetic field at the center of a current carrying a circular coil

\(B = \frac{μ_0}{4π}× \frac{2π N I}{r}\)

where μ0 = 4π × 10-7Wb/Am, N is the number of turns, I is the current intensity and r is the radius of the coil

Calculation:

Given N = 500, I = 0.30A and r = 0.06m

\(B = 10^{-7} × \frac{2\pi × 500 × 0.30}{0.06}\)

B = 1.57 × 10-3T

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