An electron is moving paralel to the Earth's surface at the equator in a direction 12 degrees south of east. Its velocity is 9.2 x 10^4 m/s and a magnetic force of 9.4 x 10^-18 N is exerted on the electron. If the magnetic field points south at this location, what is the dirction of the magnetic force on the electron and the magnitude of the magnetic field?
To determine the direction of the magnetic force on the electron and the magnitude of the magnetic field, we can use the right-hand rule for cross products in physics. The force on a charged particle moving in a magnetic field can be calculated using the formula:
F = q * (v x B),
where F represents the force, q is the charge of the particle, v is the velocity vector, and B is the magnetic field vector.
Given:
- Velocity of the electron, v = 9.2 x 10^4 m/s
- Force on the electron, F = 9.4 x 10^-18 N
- Magnetic field direction, pointing south
Step 1: Determine the direction of the magnetic force
Assuming the electron is negatively charged, we can use the right-hand rule. Point the thumb of your right hand in the direction of the velocity vector (12 degrees south of east), and curl your fingers towards the magnetic field vector (pointing south). With this orientation, your palm will face the direction of the magnetic force vector acting on the electron.
Step 2: Determine the magnitude of the magnetic field
Using the formula F = q * (v x B), we can rearrange it to find the magnitude of the magnetic field B:
|B| = |F| / (q * |v|),
where |F| is the magnitude of the force, q is the charge of the electron, and |v| is the magnitude of the velocity.
Substituting the given values:
|F| = 9.4 x 10^-18 N
q = charge of an electron = 1.6 x 10^-19 C
|v| = 9.2 x 10^4 m/s
|B| = (9.4 x 10^-18 N) / (1.6 x 10^-19 C * 9.2 x 10^4 m/s)
Simplifying the expression gives the magnitude of the magnetic field.
By following the right-hand rule, you can determine the direction of the magnetic force on the electron, and by using the formula, you can calculate the magnitude of the magnetic field.