Magnetic Field Strength Calculation in a Solenoid

How can we calculate the strength of the magnetic field at the center of a solenoid with specific dimensions and current flow? The strength of the magnetic field at the center of a 14.7 cm long solenoid with 849 turns and a current of 4.93 A is approximately 0.0357 Tesla.

When determining the strength of the magnetic field at the center of a solenoid, we can use the formula B = μ0nI, where B is the magnetic field strength, μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current flowing through the solenoid.

In this specific example, the solenoid is 14.7 cm (or 0.147 m) long and consists of 849 turns. To begin the calculation, we first need to determine the number of turns per meter, n. This is done by dividing the total number of turns (849) by the length of the solenoid in meters (0.147 m), resulting in approximately 5775.51 turns per meter.

Given that the current flowing through the solenoid is 4.93 A, we can now substitute the values into the formula B = μ0nI to find the magnetic field strength at the center of the solenoid.

Calculation:

B = (4π x 10^-7 T·m/A) x (5775.51 turns/m) x (4.93 A)

After performing the calculations, we find that:

B = 4π x 10^-7 x 5775.51 x 4.93

B ≈ 0.0357 T (or Tesla)

Therefore, the strength of the magnetic field at the center of this particular solenoid is approximately 0.0357 Tesla.

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