Final answer:
To find the magnitude and direction of the electric field at a given point on the x-axis due to an electron, we can use Coulomb's law. The magnitude of the electric field can be calculated using the formula E = k * (q / r^2), where k is the electrostatic constant, q is the charge of the electron, and r is the distance between the point and the charge. The direction of the electric field is opposite to the positive x-axis due to the negative charge of the electron.
Step-by-step explanation:
To find the magnitude and direction of the electric field at a given point due to an electron, we can use Coulomb's law. Coulomb's law states that the magnitude of the electric field at a point due to a point charge is given by:
Electric field (E) = k * (q / r^2)
Where:
- k is the electrostatic constant (8.99 x 10^9 N·m^2/C^2)
- q is the charge of the particle (in this case, the charge of the electron, which is -1.6 x 10^-19 C)
- r is the distance between the point and the charge (in this case, the distance is given as 9.39 x 10^-6 m)
Plugging in the values, we get:
Electric field (E) = (8.99 x 10^9 N·m^2/C^2) * (-1.6 x 10^-19 C) / (9.39 x 10^-6 m)^2
Calculating this will give us the magnitude of the electric field at the given point. To determine the direction, we need to consider the sign of the charge. Since the charge of the electron is negative, the electric field will point towards the electron. Therefore, the direction of the electric field at the given point will be opposite to the direction of the positive x-axis.
The magnitude of the electric field at the given point is approximately 1.83 x 10^10 N/C.