Magnetic image of a coil over a conducting surface

[mkarabiyik]

Homework Statement

If the coil in the figure is touching to an ideally conducting (σ=∞) non-magnetic steel from the A4-A5 side, what would be the magnetic field in the gap. Assume A1=A2=A3=A4=A5.

Homework Equations

The Attempt at a Solution

I have calculated that when the coil is alone, the magnetic field in the gap is

B=μ0NI/g
where g is the gap at A5

So how the results modifies when there is an image coil induced by the conducting metal.
Thanks

 

[anathema]

for your post, I appreciate your question.

When a conducting metal is placed near a coil, it can induce an image current in the metal. This image current produces its own magnetic field, which can affect the overall magnetic field in the gap of the coil. In this case, since the metal is ideally conducting, the image current will be equal in magnitude and opposite in direction to the current in the coil. This means that the total magnetic field in the gap will be the sum of the magnetic fields produced by the coil and the image current.

To calculate the magnetic field in the gap, you can use the superposition principle, which states that the total field is equal to the sum of the individual fields. In this case, the magnetic field in the gap can be calculated as:

B_total = B_coil + B_image

where B_coil is the magnetic field produced by the coil alone and B_image is the magnetic field produced by the image current.

Since the coil and the image current are equal in magnitude and opposite in direction, their magnetic fields will cancel each other out. This means that the net magnetic field in the gap will be zero.

In summary, when a conducting metal is placed near a coil, the presence of the image current will cancel out the magnetic field in the gap, resulting in a net magnetic field of zero.