Induced current and force on circular loop in varying magnetic field

[songoku]

Homework Statement

A circular loop of radius r and resistance R is placed in magnetic field given by $B(r,t)=B_o\left(1-\frac{r}{R_o}\right)e^{kt}$ where $B_o, ~k ~\text{and} ~R_o$ are positive constant and $r\leq R_o$
a) Describe qualitatively how the direction of the induced current changes
b) Find the net force experienced by the loop

Relevant Equations

$F=\int I d\vec l \times \vec B$

Faraday and Lenz Law

a) I don't think the direction of the induced current will change. Based on Lenz law, the circular loop will produce current that will oppose the varying magnetic field. Let's assume the direction of the varying magnetic field is into the page and the plane of the circular loop is perpendicular to the magnetic field so the direction of the induced current will be anticlockwise and will stay anticlockwise.

b) I think the net force will be zero due to symmetry since the opposite part of the wire will experience equal force but in opposite direction so they will cancel out

Are my answers correct? Thanks

 

[TSny]

Is there any information about the direction of the magnetic field?
How is the loop oriented in the magnetic field?
Where is the center of the loop located in the magnetic field?
Was a diagram provided with this problem?

 

[songoku]

Is there any information about the direction of the magnetic field?
How is the loop oriented in the magnetic field?
Where is the center of the loop located in the magnetic field?
Was a diagram provided with this problem?

There is no diagram and no information about all of these. The question in ##1 is all of it.

I assume it will be like this:

 

[Gavran]

a) I don't think the direction of the induced current will change. Based on Lenz law, the circular loop will produce current that will oppose the varying magnetic field. Let's assume the direction of the varying magnetic field is into the page and the plane of the circular loop is perpendicular to the magnetic field so the direction of the induced current will be anticlockwise and will stay anticlockwise.

The answer is correct, but the explanation is wrong. Your statement that the induced current generates a magnetic field which opposes the initial magnetic field is not correct. Lenz’s law states that the induced current generates a magnetic field which opposes the change of the initial magnetic field.

b) I think the net force will be zero due to symmetry since the opposite part of the wire will experience equal force but in opposite direction so they will cancel out

The answer is correct and the explanation is correct.

 

[songoku]

Thank you very much TSny and Gavran