A question about conducting loop

[electrox]

Homework Statement

A conducting loop (assumed to be infinitely thin) is being moved along time the x -axis as shownin figure 1the current in the wire is changing with i(t)=cos(wt)
the loop position 2-tm t >0

http://img3.imageshack.us/img3/9530/adszbv.jpg

Uploaded with ImageShack.uswhat is the transformer emf induced?
what is the emotional emf produced?
what is the total induced emf and the current wire?

Homework Equations

e = -df/dt

= -d (fm sin wt) / dt

= -fm w cos wt

= -fm w sin (p/2 - wt)

= fm w sin (wt-p/2)

If fm.w = em, then

e1 = em sin (wt-p/2)

If coil P has N1 turns, then the total e.m.f. induced = N1e1

= N1.em sin (wt-p/2)

The Attempt at a Solution

I know above equations but I can't solve the question also I can't relate each other . please help me

 

[KataKoniK]

Thank you for posting your question. It seems like you are having trouble understanding the concept of induced EMF in a conducting loop. Let me try to explain it to you in simpler terms.

Firstly, let's define what EMF is. EMF stands for electromagnetic force, and it is the force that causes electric charges to move in a circuit. It is measured in volts (V).

Now, when a conducting loop is moved along the x-axis, it creates a changing magnetic field around it. This changing magnetic field induces an EMF in the loop, which causes a current to flow through the loop. This is known as transformer EMF because it is caused by the changing magnetic field.

The formula for transformer EMF is given by:

e = -N1(dφ/dt)

Where N1 is the number of turns in the conducting loop and dφ/dt is the rate of change of the magnetic flux through the loop.

In your question, the current in the wire is changing with i(t) = cos(wt). This means that the magnetic flux through the loop is also changing with time. Using the formula above, we can calculate the transformer EMF induced in the loop.

e = -N1(dφ/dt) = -N1(d/dt)(B*A)

Where B is the magnetic field and A is the area of the loop.

Since the loop is being moved along the x-axis, the magnetic field will be perpendicular to the loop, and therefore, the area of the loop will be changing with time. This means that we need to take the derivative of the area with respect to time.

dA/dt = -2tm

Substituting this into the formula for transformer EMF, we get:

e = -N1(d/dt)(B*A) = -N1(B*dA/dt) = -N1(B*(-2tm)) = 2N1Btm

Now, we need to calculate the emotional EMF produced. This is the EMF that is produced due to the motion of the conducting loop. It is given by the formula:

e = -N1(dφ/dt) = -N1(d/dt)(B*A) = -N1(B*dA/dt) = -N1(B*(-2tm)) = 2N1Btm

The total induced EMF in the loop will be the sum of the transformer EMF