The magnitude of the induced electric field inside a cylindrical region is proportional to:

In summary, the conversation discusses the use of Ampere-Maxwell law versus Faraday-Maxwell law in a problem involving the magnitude of electric field. The problem statement does not involve time-varying electric flux, but does involve time-varying magnetic flux. The equation E = B * r /2 is derived, and it is confirmed that E is proportional to r. The speaker also suggests changing B to dB/dt for the equation to hold.
  • #1
hidemi
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Homework Statement
A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time. If r is the radial distance from the cylinder axis, the magnitude of the induced electric field inside the cylindrical region is proportional to

A) R
B) r
C) r²
D) 1/r
E) 1/ r²

The answer is B.
Relevant Equations
(See better interpretation in the "Attempt at a Solution" section)
I used the equation below and the attachment to rationalize.
https://www.physicsforums.com/attachments/282163
 

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  • #2
You used Ampere-Maxwell law while you should use Faraday-Maxwell Law. The problem statement asks for the magnitude of the electric field. There is no time-varying electric flux in this problem setup (so ##\frac{d\Phi_E}{dt}=0## but there is time-varying magnetic flux (linearly time varying)).
 
  • #3
\oint _{\partial \Sigma }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} }{\mathrm {d} t}}\iint _{\Sigma }\mathbf {B} \cdot \mathrm {d} \mathbf {S}

E * 2πr = - B * π r²
E = B * r /2
Therefore, E is proportional to r. Is this correct?
 
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  • #4
hidemi said:
\oint _{\partial \Sigma }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} }{\mathrm {d} t}}\iint _{\Sigma }\mathbf {B} \cdot \mathrm {d} \mathbf {S}

E * 2πr = - B * π r²
E = B * r /2
Therefore, E is proportional to r. Is this correct?
Yes the above is correct.
 
  • #5
hidemi said:
\oint _{\partial \Sigma }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=-{\frac {\mathrm {d} }{\mathrm {d} t}}\iint _{\Sigma }\mathbf {B} \cdot \mathrm {d} \mathbf {S}

E * 2πr = - B * π r²
E = B * r /2
Therefore, E is proportional to r. Is this correct?
Change B to dB/dt (= constant).
 
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Likes hidemi

Related to The magnitude of the induced electric field inside a cylindrical region is proportional to:

1. What is the meaning of "magnitude of the induced electric field"?

The magnitude of the induced electric field refers to the strength or intensity of the electric field that is created in a certain region due to the presence of a changing magnetic field.

2. What is a cylindrical region?

A cylindrical region is a three-dimensional space that is bounded by two parallel circular bases and a curved side, resembling the shape of a cylinder.

3. How is the magnitude of the induced electric field inside a cylindrical region calculated?

The magnitude of the induced electric field inside a cylindrical region is calculated using the equation E = -N(dΦB/dt), where E is the magnitude of the induced electric field, N is the number of turns in the coil, and dΦB/dt is the rate of change of the magnetic flux through the coil.

4. What is the relationship between the magnitude of the induced electric field and the changing magnetic field?

The magnitude of the induced electric field is directly proportional to the rate of change of the magnetic field. This means that as the magnetic field changes, the induced electric field also changes in magnitude.

5. What factors can affect the magnitude of the induced electric field inside a cylindrical region?

The magnitude of the induced electric field can be affected by factors such as the strength of the magnetic field, the number of turns in the coil, and the rate at which the magnetic field changes. Additionally, the material of the cylindrical region and the properties of the medium surrounding it can also have an impact on the induced electric field.

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