A solenoid 10.0 cm in diameter and 75.0 cm long is made from copper wire of diameter 0.100 cm, with very thin insulation. The wire is wound onto a cardboard tube in a single layer, with adja- cent turns touching each other. What power must be delivered to the solenoid if it is to produce a field of 8.00 mT at its center

Power = 2.22W

Explanation:

We are given;

Length of Solenoid; L = 75cm = 0.75m

Diameter of copper wire; d = 0.1 cm = 0.001m

B = 8 mT = 0.008T

From Ampere's law formula,

B = μo•I•N/L

Where;

B is magnetic field

I is current

N is number of turns

L is length of Solenoid

μo is vacuum permeability amd it has a constant value of 4π x 10^(-7) H/m

Now, let's find N.

N is given by; N = L/d

N = 0.75/0.001 = 750 turns

From earlier, B = μo•I•N/L

Thus, let's make I the subject;

I = B•L/(μo•N)

I = (0.008 x 0.75)/(4π x 10^(-7) x 750)

I = 0.006/(0.0009424778) = 6.367 A

Now, let's find the resistance; R.

The resistance; R is given by the formula;

R = ρ•N•π•d/A

Where;

ρ is resistivity of copper wire and has a value of 1.68 x 10^(-8) Ω.m

A is the area

Now area is given as; A = πd²/4

Putting this in the resistance equation gives;

R = ρ•N•π•d/(πd²/4)

This gives;

R = (4ρ•N•π•d)/(πd²)

This leads to; R = (4ρ•N)/(d)

Plugging in the relevant values, we have;

R = (4 x 1.68 x 10^(-8) x 750)/0.001

R = 0.0504 Ω

Now, we know that the formula for Power is;

P = I²R

where I is current and R is resistance.

Thus, Power = 6.637² x 0.0504 = 2.22 W

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2