Question

a 550-turn solenoid is 17 cm long. the current into it is 31 a . a 3.2 cm -long straight wire cuts through the center of the solenoid, along a diameter. this wire carries a 24 a current downward (and is connected by other wires that don't concern us).

Answer 1

The solenoid's magnetic field is calculated using its turns and length. The magnetic force on the straight wire inside the solenoid is then determined based on the magnetic field and wire's length.

In this scenario, we have a solenoid with 550 turns and a length of 17 cm, carrying a current of 31 A. Additionally, there is a straight wire, 3.2 cm long, cutting through the center of the solenoid along a diameter, and carrying a current of 24 A downward.

The magnetic field B inside a solenoid can be calculated using the formula:

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

where:

-
`\(\mu_0\)` is the permeability of free space
`(\(4\pi * 10^(-7) \, \text{T m/A}\))`,

-
`\(n\)` is the number of turns per unit length (solenoid's turns per meter),

-
`\(I\)` is the current.

First, find the number of turns per unit length (\(n\)):

`\[ n = \frac{\text{Total number of turns}}{\text{Length of solenoid}} \]`

Substitute the given values to find (n).

Next, use the magnetic field formula to find the magnetic field inside the solenoid.

The magnetic force (F) acting on the straight wire inside the solenoid, perpendicular to the magnetic field, can be calculated using the formula:

`\[ F = B \cdot I \cdot l \]`

where:

B is the magnetic field,

I is the current in the wire,

l is the length of the wire inside the solenoid.

Now, substitute the calculated magnetic field and given values to find the magnetic force acting on the wire.