Final answer:
The magnitude of the force on the electron is 6.2 x 10^-14 N, and using the right-hand rule, the direction of the force is to the south.
Step-by-step explanation:
To calculate the magnitude and direction of the force on an electron moving through a magnetic field, we use the Lorentz force equation F = q(v x B), where F is the force, q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field. The resultant force is always perpendicular to the direction of both the velocity and the magnetic field due to the cross-product.
An electron has a negative charge, so we take q to be -1.60 x 10^-19 C. Given that the electron is traveling horizontally to the east at a speed of 7.34 x 10^5 m/s and the magnetic field is vertically upward with a strength of 0.53 T, we can find the magnitude of the force as follows:
- F = |q| x v x B
- F = (1.60 x 10^-19 C) x (7.34 x 10^5 m/s) x (0.53 T)
- F = 6.2 x 10^-14 N
The direction of the magnetic force can be determined using the right-hand rule. Point your fingers in the direction of the velocity (east), and bend them towards the direction of the magnetic field (upward). Your thumb will point in the direction of the force on a positive charge, which means the force on an electron will be in the opposite direction. Therefore, the force on the electron will be directed to the south.