Final answer:
To keep a proton traveling straight between parallel metal plates in a magnetic field, a potential difference that creates an electric field to counteract the magnetic force is needed. The formula V = vBd can determine the required potential difference by balancing the magnetic force with the electric force. Using the given values, one can compute the exact potential difference.
Step-by-step explanation:
To determine the potential difference necessary to keep a proton traveling in a straight line between two horizontal parallel metal plates separated by a distance of 7.995 cm in a north-directed magnetic field of magnitude 0.779 T, we must counteract the magnetic force with an electric force. When a proton travels due east through a magnetic field directed north, the magnetic force acts in the south-to-north direction, according to the right-hand rule. By applying an electric field within the gap between the plates directed from the south plate to the north plate, we create an electric force that can balance the magnetic force.
The magnetic force on a charged particle is given by the equation Fm = qvBsin(θ), where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field direction. For a proton moving perpendicular to a magnetic field (sin(90°) = 1), this simplifies to Fm = qvB. The electric force needed to counteract the magnetic force is equal in magnitude and opposite in direction: Fe = qE, where E is the magnitude of the electric field which is equal to the potential difference V across the plates divided by the distance d between them (E = V/d).
By setting the magnetic and electric forces equal to each other (Fm = Fe), we can solve for the required potential difference: V = vBd. Substituting the provided values, we get the potential difference V = (4.09 x 105 m/s) x (0.779 T) x (7.995 x 10-2 m). After calculating, the potential difference necessary to keep the proton moving straight is V.