To find the magnitude and direction of the electron's initial acceleration, you can use the formulas for the magnetic force on a moving charge and the right-hand rule. To determine the magnitude and direction of the electric field that will keep the electron moving parallel to the wire, you can use the formula for the electric force on a charge and consider the balance between the electric and magnetic forces.
a. The magnitude of the electron's initial acceleration can be found using the formula for the magnetic force on a moving charge in a magnetic field: F = qvB, where F is the force, q is the charge, v is the velocity, and B is the magnetic field. In this case, the charge of the electron is -1.6 x 10⁻¹⁹ C, the velocity is 250 km/s (converted to m/s), and the magnetic field can be calculated using the right-hand rule for magnetic fields around a long straight wire carrying current. The magnitude of the magnetic field is given by the equation B = (μ0 x I) / (2π x r), where μ0 is the permeability of free space, I is the current in the wire, and r is the distance from the wire.
After calculating the magnitude of the magnetic field, you can substitute the values into the formula for the force to find the magnitude of the electron's initial acceleration. The direction of the acceleration will be perpendicular to both the velocity of the electron and the magnetic field, according to the right-hand rule.
b. In order for the electron to continue to travel parallel to the wire, the electric force on the electron must balance out the magnetic force. The electric force can be determined using the formula F = qE, where E is the electric field. By substituting the charge of the electron and the known acceleration, you can solve for the magnitude of the electric field. The direction of the electric field must be opposite to the direction of the electron's initial velocity in order to balance out the magnetic force and keep the electron moving parallel to the wire.