A proton is at x = 0.970 cm and is moving to the left with speed 2.00 × 106 m/s, as shown above. Point A is located at y = 0.970 cm, point B is at the origin, and point C is at y = -0.970 cm. What is the magnitude of the magnetic field produced by the proton at point B?
Question
A proton is at x = 0.970 cm and is moving to the left with speed 2.00 × 106 m/s, as shown above. Point A is located at y = 0.970 cm, point B is at the origin, and point C is at y = -0.970 cm. What is the magnitude of the magnetic field produced by the proton at point B?
Solution
The magnetic field B produced by a moving charge q at a distance r is given by the formula:
B = μ0qv/(4πr^2)
where: μ0 is the permeability of free space = 4π x 10^-7 T m/A, q is the charge of the proton = 1.6 x 10^-19 C, v is the speed of the proton = 2.00 x 10^6 m/s, r is the distance from the proton to point B = 0.970 cm = 0.970 x 10^-2 m.
Substituting these values into the formula, we get:
B = (4π x 10^-7 T m/A * 1.6 x 10^-19 C * 2.00 x 10^6 m/s) / (4π * (0.970 x 10^-2 m)^2) = (3.2 x 10^-23 T m^2/s) / (9.409 x 10^-5 m^2) = 3.4 x 10^-19 T
So, the magnitude of the magnetic field produced by the proton at point B is approximately 3.4 x 10^-19 Tesla.
Similar Questions
A proton travels at a speed of 7.20×107 m/s along the x-axis. What is the magnetic field at the point (0.00 cm, -7.00 cm, 0.00 cm) when the proton passes through the origin?
A proton is moving through a magnetic field of magnitude 4.40 × 10–3 T. The proton experiences only a magnetic force of 3.3 × 10–15 N. At a certain instant, it has a speed of 4.25 × 105 m s–1. Determine the angle (less than 90°) between the proton's velocity and the magnetic field.
The speed of the proton is 2.0 × 106 m s–1 and the magnetic field strength B is 0.35 T.(i) Show that the radius of the path is about 6 cm.
A proton moves with a velocity of = (3î − 4ĵ + ) m/s in a region in which the magnetic field is = (î + 2ĵ − ) T. What is the magnitude of the magnetic force this particle experiences?
An electron travels at a speed of 5.56×107 m/s along the z-axis. What is the magnetic field at the point (0.00 cm,7.00 cm,7.00 cm) when the electron passes through the origin?Magnitude:
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.