How Do I Solve These Complex Magnetic Fields Problems?

[Hollysmoke]

I'm having trouble with 4 questions and not sure how to go about starting to solve them. If anyone can give me help on how to approach these questions, it'd be really appreciated. I just put them all down at once rather then making separate threads. Thank you.

1) An electrical transmission line that carries a DC of 100 A West is suspended between two towers 50m apart. The dip angle is 45 degrees and the magnetic field strength is 3.0x10^-5

a) How far from the high voltage power lines do you have to be in order for the artificial magnetic field to balance Earth's magnetic field?

b) If the transmission lines are 25m above the ground and all the physical parameters remain the same, calculate the exact moment of this cancellation.

2) The two wires in a typical household extension cord are 2.4mm apart. What force per meter pushes them apart when 13.0 A. The rubber insulation has the same permeability as the air with 4pi x 10^-7

3) A bullet traveling at 400m/s picks up a charge of 20 C. What is the maximum force exerted on the bullet by Earth's magnetic field (4.5x10^-5 T)?

4) What is the magnitude and direction of the magnetic force on the proton moving vertically upward at 4.3x10^4 m/s in a 1.5-T magnetic field pointing horizontally to the west?

 

[berkeman]

-1- I don't know why they try to give you a magnetic field strength of 3*10^-5 [units?] -- you need to calculate that based on the current in the wire(s). It's also a poorly stated problem, because they only refer to one wire and no return wire at some spacing away. Whatever. How do you calculate the magnetic field around a current-carrying conductor?

(a) Do you know the magnitude of the Earth's B field?

(b) What is the exact wording of this question? What is meant by "moment"?

-2- What is the equation for the force between two current-carrying wires?

-3- Hint -- use the Lorentz force.

-4- Same hint.

 

[kyle8921]

1) To solve this problem, we need to use the equation for the magnetic field created by a current-carrying wire, which is B = (μ0I)/(2πr). We also know that the magnetic field created by the transmission lines is opposite in direction to Earth's magnetic field. So, to find the distance from the transmission lines where the two fields balance, we set the two fields equal to each other and solve for r:

(μ0I)/(2πr) = B_earth

Where I is the current (100 A), μ0 is the permeability of free space (4π x 10^-7), and B_earth is the strength of Earth's magnetic field (4.5x10^-5 T). Solving for r, we get:

r = (μ0I)/(2πB_earth)

Plugging in the values, we get r = (4π x 10^-7 x 100)/(2π x 4.5x10^-5) = 0.0044 m. So, the distance from the transmission lines where the two fields balance is 0.0044 m, or 4.4 mm.

b) To find the exact moment of cancellation, we need to consider the magnetic field created by the transmission lines at a specific point. The equation for the magnetic field at a point on the axis of a current-carrying wire is B = (μ0I)/(2πr), where r is the distance from the point to the wire. In this case, we want to find the point where the magnetic field created by the transmission lines is equal and opposite to Earth's magnetic field. So, we set the two fields equal to each other again and solve for r:

(μ0I)/(2πr) = B_earth

Solving for r, we get r = (μ0I)/(2πB_earth) = (4π x 10^-7 x 100)/(2π x 4.5x10^-5) = 0.0044 m.

This means that at a distance of 0.0044 m from the transmission lines, the two fields will cancel each other out. To find the exact moment of cancellation, we need to consider the speed at which the magnetic field is moving. The speed of the magnetic field is given by the equation v = d/t,