# Calculating Induced EMF in a Larger Solenoid Slipped Over Another Solenoid

• cuallito
In summary: Good job!In summary, the problem involves a long straight solenoid with a diameter of 3cm, 40 turns per cm, and a current of .275 A. A second solenoid with a larger diameter is placed over the first solenoid and has a diameter of 3.6cm and N=6 in part (a) and a diameter of 7.2cm and N=12 in part (b). The question asks for the emf induced in the second coil as the current in the first solenoid is ramped down to zero over 0.2 seconds. By using Faraday's law, the induced emf is calculated to be -2.93*10^-5 V in
cuallito
1. Problem statement

A very long straight solenoid has a diameter of 3cm, 40 turns per cm, and a current of .275 A. A second solenoid is with larger diameter is slipped over it with N turns per cm, and the current is ramped down to zero over 0.2 s.

a) What is the emf induced in the second coil if it has a diameter of 3.6cm and N=6?
b) The diameter is 7.2cm and N=12 ?

B=μNI

## The Attempt at a Solution

Wouldn't the answer to both (a) and (b) be zero, since the magnetic field outside a solenoid is basically zero?

Last edited:
cuallito said:
Wouldn't the answer to both (a) and (b) be zero, since the magnetic field outside a solenoid is basically zero?
No. An emf will be induced in the second solenoid as long as there is a changing magnetic flux through it. Pretty amazing. The changing magnetic field of the first solenoid induces an electric field both inside and outside the first solenoid. This induced electric field is what creates the emf in the second solenoid. But you don't need to calculate this electric field in order to work the problem.

Is the diameter of the first solenoid given?

Oh sorry, left it it out, 3cm.

So would the magnetic flux passing thru both solenoids be the same, like a transformer?

So let me take a stab at it here:

The magnetic flux from the first solenoid would be:

Φ1=BA
A=cross sectional area
B=μ*N1*I
N1=number of turns of 1st solenoid
Φ1=μ*N1*I*A

Magnetic flux thru both solenoids would be the same Φ1=Φ2

Ampere's law for 2nd solenoid:
emf=-N2*Φ/Δt
emf=-N2*μ*N1*I*A/Δt

Plugging in for (a) I get -2.93*10^-7 V
for (b) I get -5.86255*10^-7

Is that right?

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cuallito said:
Φ1=BA
A=cross sectional area
B=μ*N1*I
N1=number of turns of 1st solenoid
Φ1=μ*N1*I*A
Note that N1 is the number of turns per unit length of solenoid 1

Magnetic flux thru both solenoids would be the same Φ1=Φ2

Ampere's law for 2nd solenoid:
emf=-N2*Φ/Δt
emf=-N2*μ*N1*I*A/Δt
OK. (Faraday's law - not Ampere's law)

Plugging in for (a) I get -2.93*10^-7 V
for (b) I get -5.86255*10^-7
I do not get the same power of 10. Did you express N1 in SI units?

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Ah, so N1 would be 40/.01 = 4000 turns per meter.

So you'd get to the -5 instead of -7th power?

cuallito said:
Ah, so N1 would be 40/.01 = 4000 turns per meter.

So you'd get to the -5 instead of -7th power?
Yes, that is what I got.

## What is a solenoid over a solenoid?

A solenoid over a solenoid is a type of electromagnet in which a coil of wire is wound around a cylindrical core, creating a magnetic field. This solenoid is then placed over another solenoid, with the two coils oriented in opposite directions, to create a stronger and more uniform magnetic field.

## How do solenoids over solenoids work?

Solenoids over solenoids work by passing an electric current through the first coil, creating a magnetic field. This magnetic field then induces a current in the second coil, which reinforces the initial magnetic field. The resulting magnetic field is stronger and more uniform than that of a single solenoid.

## What are the applications of solenoids over solenoids?

Solenoids over solenoids have a wide range of applications, including in electric motors, generators, and speakers. They are also used in medical devices, such as MRI machines, and in industrial equipment, such as magnetic levitation trains.

## What are the advantages of using solenoids over solenoids?

The main advantage of using solenoids over solenoids is the stronger and more uniform magnetic field they produce. This makes them more efficient and effective in various applications. Additionally, because they use two coils, they can be designed to have a greater range of magnetic field strengths.

## What are the limitations of solenoids over solenoids?

The main limitation of solenoids over solenoids is that they require a power source to maintain the electric current and magnetic field. They also have a limited range of applications, as they are most effective at producing strong and uniform magnetic fields, rather than precise or directional fields.

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