An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?
The electron will be accelerated along the axis.
B. The electron path will be circular about the axis.
C. The electron will experience a force at 45° to the axis and hence execute a helical path.
D. The electron will continue to move with uniform velocity along the axis of the solenoid.
We know that in a current carrying long solenoid the magnetic field is only inside the solenoid and parallel to the axis. Therefore, when electron is projected with uniform velocity along the axis of a current carrying long solenoid it will experience a force due to the magnetic field in there, which will be parallel to the axis. And due to this force along the axis the electron will accelerate along the axis.
Hence, our answer will be option (a).
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A tightly-wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current i n dx.
(a) Write the magnetic field at the center of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the center of the solenoid.
(b) Verify that if l >> a, the field tends to B = μ0ni and if a >> l, the field tends to
B=. Interpret these results
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