What is the emf induced in the loop?

• BillytheKid
In summary, the conversation discusses a long solenoid with 400 turns per meter and a current of 30 A that creates a uniform magnetic field. Inside the solenoid, there is a smaller coil with 250 turns and a radius of 0.06 m. The question is about the induced EMF in the smaller coil, and the equation given is N(deltaBA/deltat). The conversation also mentions uncertainty about using this equation when there is an inside coil.
BillytheKid
A long solenoid has n = 400 turns/m and carries a current I = 30 A(1 - e-1.6t/s). Inside the solenoid and coaxial with it is a loop that has a radius R = 0.06 m and consists of N = 250 turns of wire (Fig. 3). What is the emf induced in the loop?

I know that the inuced emf is N(deltaBA/deltat) but I'm not sure what to use when there is an inside coil as well. Or maybe my the equation is wrong all together...please help

BillytheKid said:
A long solenoid has n = 400 turns/m and carries a current I = 30 A(1 - e-1.6t/s). Inside the solenoid and coaxial with it is a loop that has a radius R = 0.06 m and consists of N = 250 turns of wire (Fig. 3). What is the emf induced in the loop?

I know that the inuced emf is N(deltaBA/deltat) but I'm not sure what to use when there is an inside coil as well. Or maybe my the equation is wrong all together...please help
Long solenoids create a uniform magnetic field in their interiors, correct? Well, the equation given for the amperage... this will cause the magnetic field to change with time, your Delta B, which yields an induced EMF in the interior coil.

The equation you have is correct. To calculate the induced emf in the loop, you will need to use the formula N(deltaBA/deltat), where N is the number of turns in the loop, deltaB is the change in magnetic field, and deltat is the change in time.

In this case, the magnetic field inside the solenoid is given by B = mu0*n*I, where mu0 is the permeability of free space, n is the number of turns per unit length, and I is the current. Using this, we can calculate the change in magnetic field as deltaB = mu0*n*(I(t2) - I(t1)), where t2 and t1 are the final and initial times respectively.

Substituting the values given in the problem, we get deltaB = (4*pi*10^-7)*(400)*(30*(1-e^-1.6t2/s) - 30*(1-e^-1.6t1/s)).

Now, the change in time can be calculated as deltat = t2 - t1.

Finally, substituting these values in the formula N(deltaBA/deltat), we get the induced emf in the loop as N*[(4*pi*10^-7)*(400)*(30*(1-e^-1.6t2/s) - 30*(1-e^-1.6t1/s))]/(t2-t1).

Therefore, the induced emf in the loop is dependent on the number of turns in the loop, the change in magnetic field inside the solenoid, and the change in time.

1. What is emf and how is it related to induced in the loop?

EMF, or electromotive force, is the potential difference created by an electric field that causes charges to flow in a circuit. When a conducting loop is placed in a changing magnetic field, an EMF is induced in the loop.

2. How is the magnitude of the induced EMF determined?

The magnitude of the induced EMF is determined by the rate of change of the magnetic field through the loop. The greater the rate of change, the greater the induced EMF.

3. Can the direction of the induced EMF be predicted?

Yes, the direction of the induced EMF can be predicted using the right-hand rule. If the fingers of the right hand curl in the direction of the changing magnetic field, the thumb will point in the direction of the induced EMF.

4. How does the size and shape of the loop affect the induced EMF?

The size and shape of the loop do not directly affect the induced EMF. However, they can affect the amount of magnetic flux through the loop, which in turn affects the magnitude of the induced EMF.

5. Can the induced EMF be increased or decreased?

Yes, the induced EMF can be increased or decreased by changing the rate of change of the magnetic field through the loop or by changing the number of loops in the circuit. This is the principle behind devices such as transformers and generators.

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