A proton travels to the east at 3.5*10⁶ m/s as it enters a region of uniform magnetic field. The magnitude of the magnetic field is 0.15 T and its direction is 30° north of east. Find the magnitude of the force on the proton at the moment it enters the magnetic field.

To find the magnitude of the force on the proton, we can use the equation:

F = q * v * B * sin(θ)

where:
F is the force on the proton
q is the charge of the proton (1.6 * 10^-19 C)
v is the velocity of the proton (3.5 * 10^6 m/s)
B is the magnitude of the magnetic field (0.15 T)
θ is the angle between the velocity and the magnetic field (30°)

Plugging in the values:

F = (1.6 * 10^-19 C) * (3.5 * 10^6 m/s) * (0.15 T) * sin(30°)

We can calculate this as follows:

F = (1.6 * 10^-19 C) * (3.5 * 10^6 m/s) * (0.15 T) * sin(30°)
≈ 8.4 * 10^-13 N

Therefore, the magnitude of the force on the proton at the moment it enters the magnetic field is approximately 8.4 * 10^-13 N.

To find the magnitude of the force on the proton, we can use the formula for the magnetic force on a charged particle:

F = q * v * B * sin(theta)

Where:
F is the magnitude of the force on the proton
q is the charge of the proton (which is equal to the elementary charge, e)
v is the velocity of the proton
B is the magnitude of the magnetic field
theta is the angle between the velocity vector and the magnetic field vector

First, let's convert the given velocity into SI units. The velocity is given as 3.5 * 10^6 m/s, which is already in SI units.

Now, we can plug in the given values into the formula:

q = e = 1.6 * 10^-19 C (charge of a proton in coulombs)
v = 3.5 * 10^6 m/s
B = 0.15 T (magnitude of the magnetic field)
theta = 30° (angle between the velocity and the magnetic field)

We need to convert the angle to radians before using it in the formula:

theta = 30° * (pi / 180°) ≈ 0.5236 radians

Now we can calculate the magnitude of the force:

F = (1.6 * 10^-19 C) * (3.5 * 10^6 m/s) * (0.15 T) * sin(0.5236 radians)

Calculating this expression will give us the magnitude of the force on the proton at the moment it enters the magnetic field.