Find the magnetic induction on the solenoid axis if it is wound tightly in one layer of wire with a diameter of d = 0.8 mm

| February 24, 2021 | education

Find the magnetic induction on the solenoid axis if it is wound tightly in one layer of wire with a diameter of d = 0.8 mm with a resistance R = 100 Ohm and the voltage at the ends of its winding U = 10V.

d = 0.8 mm = 0.8 * 10-3 m.

R = 100 ohms.

U = 10 V.

μ0 = 1.25 m * 10-6 m * kg / s2 * A2.

IN – ?

The induction of the magnetic field B on the solenoid axis is determined by the formula: B = μ0 * I * n / L, where μ0 is the magnetic constant, I is the current in the solenoid winding, n is the number of turns of the solenoid, L is the length of the solenoid.

We express the length of the solenoid L by the formula: L = n * d, where d is the diameter of the solenoid winding.

We express the current strength I according to Ohm’s law: I = U / R.

The formula for determining the magnetic induction will take the form: B = μ0 * U * n / R * n * d = μ0 * U / R * d.

B = 1.25 m * 10-6 m * kg / s2 * A2 * 10 V / 100 Ohm * 0.8 * 10-3 m = 0.00015 T = 15 * 10-5 T.

Answer: the magnetic induction on the solenoid axis will be B = 15 * 10-5 T.



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