Two parallel conduction wires carry different currents I_1 = 6 A and I_2 ( to be

Question

Two parallel conduction wires carry different currents I_1 = 6 A and I_2 (to be determined), and are separated by a distance d = 20cm. A charged particle with charge q = +1.6X10^-19 C moves with speed v = 10 cm/s as shown, at a distance of d/2 to the right of the rightmost wire. (Recall that mu_0 = 4pix10^-7 N/A^2.)

1. What is the numerical value of the magnitude of the net magnetic field at the position of the charge?

2. What is the numberical value of the magnitude of the contribution to the magnetic field at the position of the charge due to the current I_1?

3. What is the numerical value of the current I_2? (Hint: Use the results from parts 1 and 2.)

4. What is the magnitude and direction of the magnetic field at the point marked P midway between the two wires?

Here are the answers:

1. 0 T

2. 4 microT

3. 2 A

4. 16 microT. into the page

Really need help on seeing how they got to these answers!! Would like to see how the formulas come into play and are used! Thanks in advance!

Explanation / Answer

Part A)

By the right hand rule, the magnetic field from the left wire would be into the page. The magnetic field from the closer wire would be out of the page. If one was greater then the other, we would have a net field either into or out of the page.

Then, from another right hand rule, we understand F = qvB Since the velocity is upward, there must not be a force applied. If there was, the charge would move toward or away from the wires. Since there is no force, there must not be a net magnetic field into or out of the field.

Thus B = 0T

Part B)

Apply B = uI/2pi(r)

B = (4pi X 10^-7)(6)/(2pi)(.3)

B = 4 X 10^-6 T which is 4.0 uT

Part C)

4 X 10^-6 = uI/(2pi)r

4 X 10^-6 = (4pi X 10^-7)(I)/(2pi)(.10)

I = 2 Amps

Part D)
B = (4pi X 10^-7)(6)/(2pi)(.1) into the page = 1.2 X 10^-5

B = (4pi X 10^-7)(2)/(2pi)(.1) into the page = 4 X 10^-6

Net = 4 X 10^-6 + 1.2 X 10^-5 = 1.6 X 10^-5 T

That is 16 X 10^-6 T which is 16 uT into the page

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