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Physics Question on Current Electricity

A long solenoid is formed by winding insulated copper wire at the rate of 20 turns per cm. The current required to produce a magnetic field of 20 mT inside the solenoid at its center would be:

A

7.0 A

B

8.0 A

C

9.0 A

D

10.0 A

Answer

9.0 A

Explanation

Solution

 The magnetic field inside a solenoid is given by:\text{ The magnetic field inside a solenoid is given by:}
B=μ0nIB = \mu_0 n I
where B=20 mT=20×10−3 T, n=20 turns/cm=2000 turns/m, and μ0=4π×10−7 T m/A.\text{where } B = 20 \, \text{mT} = 20 \times 10^{-3} \, \text{T}, \, n = 20 \, \text{turns/cm} = 2000 \, \text{turns/m}, \text{ and } \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A}.
 Solving for the current I:\text{ Solving for the current } I:I=Bμ0n=20×10−34π×10−7×2000=9.0,AI = \frac{B}{\mu_0 n} = \frac{20 \times 10^{-3}}{4 \pi \times 10^{-7} \times 2000} = 9.0 , \text{A}