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

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.