  A long solenoid has 100 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 3.24 cm perpendicular to the solenoid axis. The speed of the electron is 0.0469c (c = speed of light, equal to 2.998 × 108 m/s). Find the current i in the solenoid.

Question

A long solenoid has 100 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 3.24 cm perpendicular to the solenoid axis. The speed of the electron is 0.0469c (c = speed of light, equal to 2.998 × 108 m/s). Find the current i in the solenoid.

Step 1

Magnetic field in the solenoid is given by : help_outlineImage TranscriptioncloseB Honi _ where, n is the turns per unit length turns 104. т and n = 100 urns ст fullscreen
Step 2

We know that, force on the moving electron in a magnetic field will be: help_outlineImage Transcriptionclose(since, the electron is moving perpendicularly En = qvB to the solenoid axis) where, q is the charge v is the speed and B is the magnetic field fullscreen
Step 3

Now, the magnetic force will be equal to the centripetal f... help_outlineImage Transcriptionclosemv2 qvB r where, m is the mass of the charge v is the speed and r is the radius fullscreen

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Magnetic Effects of Current 