Question

Review To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12 cm in diameter and 60 cm in length. You would like a 2.0 −A current to produce a 2.6 −kG magnetic field inside your solenoid. Part A What is the total length of wire you will need to meet these specifications? Express your answer using two significant figures.

Answer 1

46.80 m

Explanation:

Given:

Magnetic field, B = 2.6 kG = 2600 G = 0.26T

Diameter of the plastic tube = 12 cm = 0.12m

Length of the plastic tube = 60 cm

Current, I = 2 A

The formula for the magnetic field (B) at the center of a solenoid is calculated as:

`B=(\mu_oNI)/(L)`

where,

I = current

N = Turns

L = Length

`\mu_o`= permeability of the free space

on substituting the values in the above equation, we get

`0.26=(4\pi *10^(-7)* N* 2)/(0.6)`

or

N = 62070.42 Turns

also, each turn is a circumference of the plastic tube.

The circumference of the plastic tube, C = 2π×0.12 = 0.7539 m

Thus,

The total length of the wire required, L = (62070.42) × 0.7539 m = 46799.99 ≈ 46800 m = 46.80 km