What is the Radius of a Long Solenoid with a Given Induced Electric Field?

In summary, the equation B = 5.0t T represents the magnetic field strength within a long solenoid, where t is time in seconds. The induced electric field outside the solenoid is 11 V/m at a distance of 2.0m from the axis. To find the radius of the solenoid, one must use the equation E_inside = r/2 |dB/dt| and assume that the magnetic flux through the 2.0m circle only extends over the cross-sectional area of the solenoid.
  • #1
raisen
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Homework Statement



For a long solenoid, the magnetic field strength within the solenoid is given by the equation B = 5.0t T, where t is time in seconds. If the induced electric field outside the solenoid is 11 V/m at a distance 2.0m from the axis of the solenoid, find the radius of the solenoid.

Homework Equations



E_inside = r/2 |dB/dt|


The Attempt at a Solution



I know how to calculate the electric field outside the solenoid, but how can I associate the magnetic field inside of it with the electric field outside?
 
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  • #2
raisen said:

Homework Statement



For a long solenoid, the magnetic field strength within the solenoid is given by the equation B = 5.0t T, where t is time in seconds. If the induced electric field outside the solenoid is 11 V/m at a distance 2.0m from the axis of the solenoid, find the radius of the solenoid.

Homework Equations



E_inside = r/2 |dB/dt|


The Attempt at a Solution



I know how to calculate the electric field outside the solenoid, but how can I associate the magnetic field inside of it with the electric field outside?

Assume that the magnetic flux through the 2.0 m circle extends only over the cross-sectional area of the solenoid.
 

1. What is a long solenoid?

A long solenoid is a cylindrical coil with a length much greater than its diameter. It is typically made of a conducting material and is used in various applications, such as electromagnets and inductors.

2. What is the formula for calculating the radius of a long solenoid?

The formula for calculating the radius of a long solenoid is r = (μ_0 * N * I) / (2 * π * B), where r is the radius, μ_0 is the permeability of free space, N is the number of turns in the solenoid, I is the current flowing through the solenoid, and B is the magnetic field strength.

3. How does the radius of a long solenoid affect its magnetic field?

The radius of a long solenoid directly affects its magnetic field strength. As the radius increases, the magnetic field strength decreases, and vice versa. This relationship is described by the formula B = μ_0 * N * I / L, where B is the magnetic field strength, μ_0 is the permeability of free space, N is the number of turns in the solenoid, I is the current flowing through the solenoid, and L is the length of the solenoid.

4. Can the radius of a long solenoid be changed?

Yes, the radius of a long solenoid can be changed. It can be altered by changing the number of turns in the coil, the current flowing through the solenoid, or the magnetic field strength. However, the length of the solenoid remains constant.

5. What are some real-world applications of long solenoids?

Long solenoids have many practical applications in various industries. They are commonly used in electromagnets, which are used in motors, generators, and speakers. They are also used in inductors, which are used in power supplies and filters. Other applications include particle accelerators, magnetic resonance imaging (MRI) machines, and electromagnetic levitation systems.

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