Question

A long solenoid that has 1 125 turns uniformly distributed over a length of 0.405 m produces a magnetic field of magnitude 1.00 × 10?? T at its center. What current is required in the windings for that to occur? Part 1 of 3 - Conceptualize We estimate the current in the windings to be on the order of one ampere. The field is larger than that typically produced by a single wire because of the many turns, not because the current is very large. Part 2 of 3 - Categorize We will use the equation for the magnitude of the magnetic field at the center of a solenoid to determine the current. Part 3 of 3 - Analyze The magnetic field at the center of a solenoid of length ? with N turns carrying current I is given by B = ??(N/?)I, so solving for the current and substituting the given values, we have I = B? / ??N = (( × 10?? T)( m)) / ((4? × 10??? T · m/A)( )) = mA.

          A long solenoid that has 1 125 turns uniformly distributed over a length of 0.405 m produces a magnetic field of magnitude 1.00 × 10?? T at its center. What current is required in the windings for that to occur?

Part 1 of 3 - Conceptualize
We estimate the current in the windings to be on the order of one ampere. The field is larger than that typically produced by a single wire because of the many turns, not because the current is very large.

Part 2 of 3 - Categorize
We will use the equation for the magnitude of the magnetic field at the center of a solenoid to determine the current.

Part 3 of 3 - Analyze
The magnetic field at the center of a solenoid of length ? with N turns carrying current I is given by
B = ??(N/?)I,
so solving for the current and substituting the given values, we have
I = B? / ??N
= (( × 10?? T)( m)) / ((4? × 10??? T · m/A)( )) = mA.

A long solenoid that has 1 125 turns uniformly distributed over a length of 0.405 m produces a magnetic field of magnitude 1.00 × 10?? T at its center. What current is required in the windings for that to occur?

Part 1 of 3 - Conceptualize
We estimate the current in the windings to be on the order of one ampere. The field is larger than that typically produced by a single wire because of the many turns, not because the current is very large.

Part 2 of 3 - Categorize
We will use the equation for the magnitude of the magnetic field at the center of a solenoid to determine the current.

Part 3 of 3 - Analyze
The magnetic field at the center of a solenoid of length ? with N turns carrying current I is given by
B = ??(N/?)I,
so solving for the current and substituting the given values, we have
I = B? / ??N
= (( × 10?? T)( m)) / ((4? × 10??? T · m/A)( )) = mA.

Added by Douglas S.

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