The Earth's magnetic field above the Earth's equator is about 10^-4 north. If a proton is intially moving downward at 5*10^5 m/s, it will?

A. curve east, making a circle with r= 50 m.
B. curve west, making a circle with r=50 cm
C. curve east, making a circle with r= 3 cm
D. curve west, making a circle with r= 3 cm

To determine the direction and radius of the proton's circular path, we need to apply the right-hand rule for moving charges in magnetic fields.

The right-hand rule states that if you point your right thumb in the direction of the moving positive charge (proton in this case), and curl your fingers in the direction of the magnetic field, then your palm will face the direction of the resulting force on the charge.

Given that the Earth's magnetic field at the equator is about 10^-4 north, we know the direction of the magnetic field is northward.

So, let's apply the right-hand rule:

1. Point your right thumb downward to represent the motion of the proton.
2. Curl or rotate your fingers in a counterclockwise motion to represent the northward magnetic field.

As per the right-hand rule, your palm will face east. This implies that the resulting force on the proton will be directed towards the east. This force is responsible for curving the proton's path.

Now, let's determine the radius of the circular path:

The force on a charged particle moving through a magnetic field can be calculated using the equation:

F = q * v * B

Where:
F: Force
q: Charge of the particle (in this case, a proton - 1.6 * 10^-19 C)
v: Velocity of the particle (5 * 10^5 m/s)
B: Magnetic field strength (10^-4 T)

Substituting the values into the equation:

F = (1.6 * 10^-19 C) * (5 * 10^5 m/s) * (10^-4 T)

After performing the multiplication, we get:

F = 8 * 10^-14 N

This is the force acting on the proton.

The centripetal force required to keep the proton in a circular orbit can be calculated using the equation:

F = (m * v^2) / r

Where:
m: Mass of the proton (1.67 * 10^-27 kg)
v: Velocity of the proton (5 * 10^5 m/s)
r: Radius of the circular path (unknown)

Rearranging the equation to solve for r:

r = (m * v) / F

Substituting the values:

r = (1.67 * 10^-27 kg) * (5 * 10^5 m/s) / (8 * 10^-14 N)

After performing the multiplication and division, we get:

r = 5.1875 * 10^-8 m

This radius is approximately 3 cm. Therefore, the correct answer is:

C. curve east, making a circle with r = 3 cm.