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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.?