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Question
An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?
Options
The electron will be accelerated along the axis.
The electron path will be circular about the axis.
The electron will experience a force at 45° to the axis and hence execute a helical path.
The electron will continue to move with uniform velocity along the axis of the solenoid.
Solution
The electron will continue to move with uniform velocity along the axis of the solenoid.
Explanation:
A solenoid consists of a helical winding of wire on a cylinder, usually circular in cross-section. There can be hundreds or thousands of closely spaced turns, each of which can be regarded as a circular loop. There may be several layers of windings.
Magnetic field due to solenoid B = μ0nl Direction of the field inside the solenoid is parallel to the axis, obtained by right-hand thumb rule as shown in figure.
F = q(v × B)
F = qvB*sinθ
Now, here an electron is moving in magnetic field of solenoid, so the concept of magnetic force comes into existence.
When an electron is projected with uniform velocity along the axis of a current carrying a long solenoid, then the magnetic force due to the magnetic field acting on the electron will be F = – evB sin 180° = 0 (either velocity is parallel to magnetic field or anti-parallel or 0 = 0° or 180° in both cases F = 0). The electron will continue to move with uniform velocity or will go undeflected along the axis of the solenoid.
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