Determining the Direction of Current Flow in Parallel Wires

[jacksonwiley]

1. Homework Statement [/b]
In the figure, two parallel wires carry a current I in opposite directions. A rectangular loop is midway between the wires. The current I is decreasing. The induced current through the resistor R is:
A: Zero
B: from b to a
C: from a to b

Homework Equations

The Attempt at a Solution

i know that in order to find out which way the current is flowing i need to use the right hand rule, but i also need to know if the magnetic field is flowing out or going into the page? I'm not quite sure how i would approach determining that.

 

[berkeman]

View attachment 70561

1. Homework Statement [/b]
In the figure, two parallel wires carry a current I in opposite directions. A rectangular loop is midway between the wires. The current I is decreasing. The induced current through the resistor R is:
A: Zero
B: from b to a
C: from a to b

Homework Equations

The Attempt at a Solution

i know that in order to find out which way the current is flowing i need to use the right hand rule, but i also need to know if the magnetic field is flowing out or going into the page? I'm not quite sure how i would approach determining that.

Welcome to the PF.

For the right wire, your right hand wraps around it from above, with your thumb pointing in the direction of the current. Which way do your fingers go through the inner wire loop?

For the left wire, wrap your right hand around it from above with your thumb pointing in the direction of the current. Which way do your fingers go through the inner wire loop?

So given the situation, which way does the superposition of the two B-fields from the outer wires go through the inner loop? And you are told the B-field is decreasing, so in what direction is the ΔB? What does that tell you about the induced current in the inner loop?

 

[jacksonwiley]

for the right wire: clockwise
left: counterclockwise

so they go away from each other in the inner loop;
if i remember correctly the direction of B would be out of the page; I'm still a little lost on how to tell which way the current that is induced would flow

 

[berkeman]

for the right wire: clockwise
left: counterclockwise

?? The B-field will either be down into the page or up out of the page for the center loop...

 

[jacksonwiley]

?? The B-field will either be down into the page or up out of the page for the center loop...

oh i confused the different right hand rules. so they're both into the page. but then which rule do i use to determine the current ?

 

[berkeman]

oh i confused the different right hand rules. so they're both into the page. but then which rule do i use to determine the current ?

Correct. Use Faraday's Law to determine the voltage induced in the inner loop by the changing magnetic field...