The magnetic field of the Earth is 0.60 x 10-4 T in a certain location.
a) What will be in Newtons the force on a completely ionized carbon atom (Z = 6, A = 12) traveling with the solar wind with a velocity of 10.50 x 103 m/s perpendicular to the magnetic field?
b) How fast must the ionized carbon atom be moving (m/s) so that its weight is exactly balanced by the magnetic force acting on it? Express your answer in m/s.
To determine the force on a completely ionized carbon atom traveling with the solar wind perpendicular to the magnetic field, we can use the equation for the magnetic force on a moving charged particle.
a) The formula for the magnetic force (F) on a charged particle moving in a magnetic field is given by:
F = q * v * B
Where:
F is the magnetic force,
q is the charge of the particle,
v is the velocity of the particle,
B is the magnetic field strength.
Since we are considering a completely ionized carbon atom, we know that the charge (q) of the ion is equal to the magnitude of the charge of an electron (1.6 x 10^-19 C) multiplied by the atomic number (Z = 6).
q = Z * e
q = 6 * (1.6 x 10^-19 C)
q = 9.6 x 10^-19 C
The velocity (v) of the carbon atom is given as 10.50 x 10^3 m/s, and the magnetic field strength (B) is 0.60 x 10^-4 T.
Substituting these values into the equation for the magnetic force:
F = (9.6 x 10^-19 C) * (10.50 x 10^3 m/s) * (0.60 x 10^-4 T)
Evaluating this expression will give you the force (F) on the carbon atom in Newtons.
b) To determine how fast the ionized carbon atom must be moving for its weight to be exactly balanced by the magnetic force, we need to equate the magnetic force with the weight force.
The weight of the carbon atom can be calculated using the equation:
Weight = mass * acceleration due to gravity
Since the carbon atom is ionized, we only need to consider the mass of the carbon nucleus, which is given by the atomic mass (A = 12) multiplied by the mass of a proton.
mass of carbon nucleus = A * mass of a proton
mass of carbon nucleus = 12 * (1.67 x 10^-27 kg)
mass of carbon nucleus = 2.004 x 10^-26 kg
The acceleration due to gravity, denoted as g, is approximately 9.8 m/s^2.
So, we can calculate the weight of the carbon atom using:
Weight = (2.004 x 10^-26 kg) * (9.8 m/s^2)
Now we equate the weight with the magnetic force:
(2.004 x 10^-26 kg) * (9.8 m/s^2) = (q) * (v) * (B)
Solving this equation for the velocity (v) will give you the required speed of the ionized carbon atom in meters per second.