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oneofmany850

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## Homework Statement

In a device called a betatron, charged particles in a vacuum are accelerated by the electric

field E that necessarily accompanies a time-dependent magnetic field B(t).

Suppose that, in cylindrical coordinates, the magnetic field throughout the betatron at

time t can be approximated by

$$B = Kr^nt e_z$$

where K and n are positive constants. Assuming that the companion electric field takes the

form

$$E = E_φ(r) e_φ$$

express E in terms of r, K and n.

What mathematical feature of the electric field makes it impossible to define an

electrostatic potential field in this case? Explain your answer in two or three sentences.

## Homework Equations

## The Attempt at a Solution

Using Faradays law I get

$$E= -\frac{1}{2} Kr^{n+1} e_\phi$$

I'm not sure which feature of the field makes it impossible to define an electrostatic potential field. I'm thinking it might be that the E field is not conservative but I'm not sure why. Also the field is being generated by moving charges so I'm not sure how that can generate an electrostatic field. I wondered if the power of r had something to do with it.?