Final Exam, Question 2
An infinite straight wire runs down the z-axis at the center of an infinite
solenoid of radius R, with n turns per unit length. The wire carries current
I0 in the kˆ direction, and the solenoid carries current I1 clockwise about kˆ .
Express answers using ıˆ ˆkˆ notation in terms of the variables above and physical
constants.
1. What is the piece-wise magnetic field ~B(x) along the positive x-axis in the
regions 0 < x < R and x > R?
2. A charge q > 0 of mass m circles the wire inside the solenoid at radius r
in the xy-plane. What is the speed of the charge?
3. Both currents are now turned off and the charge begins to move in a
straight line in the ıˆ direction, and then escapes through a gap in the
solenoid (assume its speed is unchanged). It then enters a uniform electric
field −E0ıˆ (with E0 > 0). How far does it travel through the electric field
before coming to rest?
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