How to Find Magnetic Flux and EMF in a Moving Loop Near a Current-Carrying Wire?

[leonne]

Homework Statement

square loop of wire (side a) lies on a table a distance S from very long straight wire which carries current I
A) find flux of B
B) if someone now pulls the loop away from wire at speed V what emf is generated

Homework Equations

The Attempt at a Solution

I just have some questions about this problem
A)flux=$$\int$$ B.da B=uI/2pieS
flux=uI/2pie $$\int$$ 1/s (ads) my question is why did da become ads? they integrate it from s to s+a

B)$$\epsilon$$=-d$$\phi$$/dT
$$\epsilon$$=-uIa/2pie(d/dt)ln(s+a/s) ds/dt=v
$$\epsilon$$=uIa/2pie((1/s+a )ds/dt-1/s(ds/dt) also i have no idea how the got this line.
thanks

 

[mark726]

for any help!

Hello! To answer your first question, da becomes ads because it represents the infinitesimal area element of the square loop. As you integrate from s to s+a, the area element changes from s to s+a, hence the integration of ads.

For part B, the equation for emf can be derived from Faraday's law, which states that the induced emf is equal to the negative rate of change of magnetic flux. In this case, we are considering the magnetic flux through the square loop, which is given by the equation you provided in part A. The negative sign comes from the direction of the induced current, which will oppose the change in magnetic flux.

To solve for the emf, we can substitute the value of ds/dt (which is equal to the speed v at which the loop is being pulled away) into the equation. Then, we can simplify to get the final equation for emf.

I hope this helps! Let me know if you have any further questions.