Betatron, derivation of expressions

In summary, the conversation discusses a problem with question 5 on a physics exam paper. The problem involves calculating work using the equations for electromotive force and force. The mistake is that the force is changing direction twice during the cycle, so the area of the loop needs to be considered twice, resulting in the appearance of the number 4 in the equation.
  • #1
Gloyn
41
0
Hi!

I've got a problem with question 5 on this paper:

http://www.freeexampapers.com/past_papers.php?l=Past_Papers%2FAEA%2FPhysics%2F2006/

Download AEA-PHYS-PP-MayJune-2006-AEA-Paper-1342.pdf.

Starting from b) i), we got that:

ε=Δ∅/Δt → W=εe

Where W is denotes work, ε is e.m.f

Also, for ii) work can be written as:

W=2∏rF

in iv) we use F=Δp/Δt=2erΔB/Δt

as during one cycle mementum changes its direction to the opposite twice. From all that we got:

Δ∅=4∏r^2ΔB

Where 4 comes from? It should be deltaB times area of loop. I tried to check it if 2s does not cancel each other but they don't, where's the mistake?
 
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  • #2
The mistake is that you have not taken into account the fact that the force is changing direction twice during the cycle. Since the force is changing direction, the area of the loop needs to be considered twice - once when the force is in one direction and again when it is in the other direction. This is why the 4 appears in the equation.
 

FAQ: Betatron, derivation of expressions

What is a betatron?

A betatron is a type of particle accelerator that uses electromagnetic induction to accelerate electrons to high speeds.

How does a betatron work?

A betatron works by using a series of alternating magnetic fields to accelerate electrons in a circular path. As the electrons gain speed, they emit synchrotron radiation, causing them to lose energy. To maintain the acceleration, the magnetic fields must be constantly adjusted.

What are the key components of a betatron?

The key components of a betatron include a vacuum chamber, an electromagnet, an alternating current power source, and a target for the accelerated electrons to collide with.

What are some common applications of betatrons?

Betatrons are commonly used in medical settings for radiation therapy, as well as in industrial settings for material testing and non-destructive testing.

How are expressions for betatron derived?

The expressions for betatron are derived through mathematical analysis and calculations using the principles of electromagnetism and special relativity. This involves solving equations for the energy and acceleration of the electrons in the betatron.

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