How to calculate magnetic induction just beyond the end of the magnet?

In summary, the limit for the magnetic induction just beyond the end of a bar magnet on its axis is given by B = (μ/4π)(4rml)/(r^2-l^2)^2, where r → l. However, when r is approximately equal to l, the solution obtained from Wolfram Alpha is infinity. This is because the expression was derived in the limit r >> l and cannot be applied when r ≈ l.
  • #1
Lotto
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Homework Statement
Calculate magnetic induction just beyond the end of a bar magnet on its axis
Relevant Equations
$$B=\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2},$$ where r → l.
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  • #2
Lotto said:
Homework Statement:: Calculate magnetic induction just beyond the end of a bar magnet on its axis
Relevant Equations:: $$B=\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2},$$ where r → l.

I know I should use a limit $$B=\lim_{r\to l}{\frac{\mu}{4\pi}\cdot \frac{4rml}{{\left({r}^2-l^2\right)}^2}},$$,but in Wolfram I get a weird solution. https://www.wolframalpha.com/input?i2d=true&i=Limit[Divide[4rl,Power[\(40)Power[r,2]-Power[l,2]\(41),2]],r->l]

What is the solution? It shouldn't be infinity.
According to the expression you quoted, it should be infinity. Note that you are asked to find the magnetic induction just beyond the end of the magnet, not at the end of the magnet. Also, I think your expression was derived in the limit ##r>>l## so you can't do much with it when ##r\approx l##. You need to go back to the original expression from which your equation was derived and see what you get when you substitute ##r=l+\epsilon## with ##\epsilon/l <<1##.
 

FAQ: How to calculate magnetic induction just beyond the end of the magnet?

1. What is magnetic induction?

Magnetic induction, also known as magnetic flux density, is a measure of the strength of a magnetic field at a specific point in space.

2. How is magnetic induction calculated?

Magnetic induction can be calculated using the formula B = μ0 * (M/2πr^3), where B is the magnetic field strength, μ0 is the permeability of free space, M is the magnetic moment of the magnet, and r is the distance from the magnet.

3. What is the significance of calculating magnetic induction just beyond the end of the magnet?

Calculating magnetic induction just beyond the end of the magnet can help determine the strength and direction of the magnetic field, which is important for understanding the behavior of magnets and their interactions with other objects.

4. Are there any other factors that can affect the calculation of magnetic induction?

Yes, factors such as the shape and size of the magnet, the material it is made of, and the presence of other magnetic fields in the surrounding area can also affect the calculation of magnetic induction.

5. Can magnetic induction be measured experimentally?

Yes, magnetic induction can be measured using a device called a magnetometer, which can detect and measure the strength of magnetic fields at different points in space.

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