A circular coil has a 15.0 cm radius and consists of 30.0 closely wound turns of wire. An externally produced magnetic field of magnitude 2.60 mT is perpendicular to the coil. (a) If no current is in the coil, what magnetic flux links its turns? (b)When the current in the coil is 2.80 A in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Calculate the Magnetic Flux

1. **Identify the given values:**
- Radius of the coil, \( r = 15.0 \, \text{cm} = 0.15 \, \text{m} \)
- Number of turns, \( N = 30 \)
- Magnetic field strength, \( B = 2.60 \, \text{mT} = 2.60 \times 10^{-3} \, \text{T} \)
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