Question

An electron and a proton are both traveling 5e6 m/s perpendicular to a magnetic field of strength 3.4 T. What is the ratio of the radius of the electrons orbit, R1, to the radius of the protons orbit, R2? R1 = 2534.43 R2 R1 = 1836.15 R2 R1 = 3.24e-3 R2 R1 = 5.45e-4 R2

Answer 1

To find the ratio of the radii of the orbits, we need to first determine the radius of the electron's orbit (R1) and the radius of the proton's orbit (R2). The formula to calculate the radius of the orbit in a magnetic field is:

R = (m * v) / (q * B)

where m is the mass, v is the velocity, q is the charge, and B is the magnetic field strength.

For an electron:
m1 = 9.11e-31 kg (mass of electron)
q1 = 1.6e-19 C (charge of electron)

For a proton:
m2 = 1.67e-27 kg (mass of proton)
q2 = 1.6e-19 C (charge of proton)

The velocities and magnetic field strength are the same for both:

v = 5e6 m/s (velocity)
B = 3.4 T (magnetic field strength)

Now, we can calculate the radii:

R1 = (m1 * v) / (q1 * B)
R2 = (m2 * v) / (q2 * B)

To find the ratio R1/R2, we can simply divide R1 by R2:

R1/R2 = [(m1 * v) / (q1 * B)] / [(m2 * v) / (q2 * B)]

Since q1 = q2 and v and B are the same for both particles, we can simplify the ratio to:

R1/R2 = m1 / m2

Now, plug in the values:

R1/R2 = (9.11e-31 kg) / (1.67e-27 kg) ≈ 5.45e-4

So, the answer is R1 = 5.45e-4 R2.