Lorentz force and magnetic force on current-carrying wire

[mustang]

Problem 1.
A proton moves perpandicularly to a magnetic field that has a magnitude of 4.70*10^-2 T.
What is the speed of the particle if the magnitude of the magnetic force on it is 2.12*10^-14 N? Answer in m/s.
Note: What formula should I use?

Problem 4.
A proton moves straight upward (away from the ground) through a uniform magnetic field that points from east to west and has a magnitude of 4.7 T.
a. If the proton moves with a speed 1.5*10^7 m/s through this field, what is the magnitude of the force acting on it? Answer in N.
Note: What formula should I use?

Problem 8.
The magnetic force on a straight 0.37m segment of wire carrying a current of 4.5 A is 0.60 N.
What is the magnitude of the component of the magnetic field that is perpendicular to the wire? Answer in T.
Note: What should i do first?

Problem 10.
Given: g=9.81m/s^2.
A thin 2.18m long copper rod in a uniform magnetic field has a mass of 52.2g. When the rod carries a current of 0.260 A, it floats in the magnetic field.
What is the field strength of the magnetic field? Answer in T.
NOte: Where do i start?

 

[quantumdude]

Originally posted by mustang
Problem 1.
A proton moves perpandicularly to a magnetic field that has a magnitude of 4.70*10^-2 T.
What is the speed of the particle if the magnitude of the magnetic force on it is 2.12*10^-14 N? Answer in m/s.
Note: What formula should I use?

Problem 4.
A proton moves straight upward (away from the ground) through a uniform magnetic field that points from east to west and has a magnitude of 4.7 T.
a. If the proton moves with a speed 1.5*10^7 m/s through this field, what is the magnitude of the force acting on it? Answer in N.
Note: What formula should I use?

Take a close look at the equation for the magnetic force on a moving charged particle.

Problem 8.
The magnetic force on a straight 0.37m segment of wire carrying a current of 4.5 A is 0.60 N.
What is the magnitude of the component of the magnetic field that is perpendicular to the wire? Answer in T.
Note: What should i do first?

Take a close look at the equation for the magnetic force on a current-carrying wire.

Problem 10.
Given: g=9.81m/s^2.
A thin 2.18m long copper rod in a uniform magnetic field has a mass of 52.2g. When the rod carries a current of 0.260 A, it floats in the magnetic field.
What is the field strength of the magnetic field? Answer in T.
NOte: Where do i start?

Draw a free body diagram, and balance the forces.

 

[M98Ranger]

Problem 1: To solve this problem, you can use the formula F = qvB, where F is the magnetic force, q is the charge of the particle (in this case, the charge of a proton is 1.6*10^-19 C), v is the velocity of the particle, and B is the magnetic field strength. Rearrange the formula to solve for v, and plug in the given values to get v = 1.34*10^5 m/s.

Problem 4: To solve this problem, you can use the formula F = qvB, where F is the magnetic force, q is the charge of the particle (in this case, the charge of a proton is 1.6*10^-19 C), v is the velocity of the particle, and B is the magnetic field strength. Plug in the given values to get F = 1.12*10^-12 N.

Problem 8: To solve this problem, you can use the formula F = ILBsinθ, where F is the magnetic force, I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the wire and the magnetic field. In this case, θ is 90 degrees since the wire is perpendicular to the field. Rearrange the formula to solve for B, and plug in the given values to get B = 0.16 T.

Problem 10: To solve this problem, you can use the formula F = mg = ILBsinθ, where F is the magnetic force, m is the mass of the rod, g is the acceleration due to gravity, I is the current, L is the length of the rod, B is the magnetic field strength, and θ is the angle between the rod and the magnetic field. In this case, θ is also 90 degrees since the rod is perpendicular to the field. Rearrange the formula to solve for B, and plug in the given values to get B = 0.13 T.