A proton moves perpendicularly to a magnetic field that has a magnitude of 6.48 ´ 10^-2 T. A magnetic force of 7.16 ´ 10^-14 N is acting on it. If the proton moves a total distance of 0.500 m in the magnetic field, how long does it take for the proton to move across the magnetic field? If the magnetic force is directed north and the magnetic field is directed upward, what was the proton’s velocity?

To solve this problem, we can use the equation that relates the magnetic force on a moving charged particle to its velocity and the magnetic field strength.

The equation is:

F = q * v * B

Where F is the magnetic force, q is the charge of the particle (in this case, the charge of the proton), v is the velocity of the particle, and B is the magnetic field strength.

Using this equation, we can solve for the velocity of the proton:

v = F / (q * B)

Plugging in the given values:

v = (7.16 ´ 10^-14 N) / ((1.6 ´ 10^-19 C) * (6.48 ´ 10^-2 T))

Calculating this gives:

v ≈ 1.74 ´ 10^5 m/s

Next, we can use the given distance the proton traveled and its velocity to find the time it took to move across the magnetic field.

We can use the formula:

time = distance / velocity

Plugging in the given values:

time = 0.500 m / (1.74 ´ 10^5 m/s)

Calculating this gives:

time ≈ 2.87 ´ 10^-6 s

So, it takes approximately 2.87 ´ 10^-6 seconds for the proton to move across the magnetic field.

The velocity of the proton is approximately 1.74 ´ 10^5 m/s.