Question

Given that the solenoid L has 1134 turns with 0.1 m in length and its resistance is zero, find the magnetic field inside the solenoid.

Answer 1

The magnetic field inside the solenoid is 0.0204 T

How to find magnetic field?

To find the magnetic field inside the solenoid, we can use Ampere's Law, which relates the magnetic field in the solenoid (B) to the current (I) passing through the solenoid and the number of turns per unit length (n).

The formula for the magnetic field inside a solenoid is given by:

`\[ B = \mu_0 \cdot n \cdot I \]`

where:

B = magnetic field in teslas (T),

μ₀ = permeability of free space (
`\(4\pi * 10^(-7) \, \text{T}\cdot\text{m/A}\)`),

n = number of turns per unit length of the solenoid,

I = current in amperes (A).

First, we need to calculate n, which is the number of turns per meter. Given that the solenoid has 1134 turns and is 0.1 m in length, n is calculated as:

`\[ n = \frac{\text{Number of turns}}{\text{Length}} = \frac{1134}{0.1 \, \text{m}} \]`

Next, find the current I flowing through the solenoid.

There is a series-parallel circuit with resistances of 50 Ω, 150 Ω, and 50 Ω.

The two 50 Ω resistors are in parallel, so their combined resistance
`\( R_{\text{combined}} \)` is given by:

`\[ \frac{1}{R_{\text{combined}}} = (1)/(50 \, \Omega) + (1)/(50 \, \Omega) \]`

`\[ R_{\text{combined}} = (50 \, \Omega)/(2) = 25 \, \Omega \]`

Now, this combined resistance is in series with the 150 Ω resistor, so the total resistance
`\( R_{\text{total}} \)` is:

`\[ R_{\text{total}} = R_{\text{combined}} + 150 \, \Omega = 25 \, \Omega + 150 \, \Omega \]`

Finally, using Ohm's Law (
`\( V = I \cdot R \)`), find the current I provided by the 250 V battery:

`\[ I = \frac{V}{R_{\text{total}}} \]`

The combined resistance of the two parallel 50 Ω resistors is 25 Ω, and the total resistance of the circuit, including the series 150 Ω resistor, is 175 Ω.

The current flowing through the circuit, provided by the 250 V battery, is approximately 1.43 A.

With 1134 turns and a length of 0.1 m, the number of turns per unit length (n) for the solenoid is 11340 turns per meter.

Using Ampere's Law, the magnetic field inside the solenoid is approximately 0.0204 T (teslas).