GOAL Calculate the magnitude and direction of a magnetic force. PROBLEM A proton

Question

GOAL Calculate the magnitude and direction of a magnetic force. PROBLEM A proton moves with a speed of 1.00 x 105 m/s through Earth's magnetic field, which has a value of 55.0 ? T at a particular location, when the proton moves eastward, the magnetic force acting on it is directed straight upward, and when it moves northward, no magnetic force acts on it. (a) What is the direction of the magnetic field, and (b) what is the strength of the magnetic force when the proton moves eastward? (c) Calculate the gravitational force on the proton and compare it with the magnetic force. Compare it also with the electric force if there were an electric field with a magnitude equal to E 1.50 x 102 N/C at that location, a common value at Earth's surface. Note that the mass of the proton is 1.67 x 1027 kg. STRATEGY The direction of the magnetic field can be found from an application of the right-hand rule, together with the fact that no force is exerted on the proton when it's traveling north. Substituting into the magnitude of magnetic force equation yields the magnitude of the magnetic field SOLUTION (A) Find the direction of the magnetic field No magnetic force acts on the proton when it's going north, so the angle such a proton makes with the magnetic field direction must be either 0 or 180°. Therefore, the magnetic field B must point either north or south. Now apply the right-hand rule. When the particle travels east, the magnetic force is directed upward. Point your thumb in the direction of the force and your fingers in the direction of the velocity eastward. When you curl your fingers, they point north, which must therefore be the direction of the magnetic field. (B) Find the magnitude of the magnetic force Substitute the given values and the charge of a proton into the magnetic force magnitude equation. From part F-qb sin ?-(1.60 x 10-19 C)(1.00 x 105 m/s) x (55.0 106 T) sin (90.0°) 8.80 x 10-19 N

Explanation / Answer

part B:

magnetic force F = q v B sin theta

for proton q =1.6 *10^-19 C

F = 1.6*10^-19 * 1.29 *10^5 * 50.1*10^-6

F = 1.034 *10^-18 N

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part C:

grav force F = mg

F = 1.67 *10^-27 * 10  

F grav = 1.67 *10^-26 N
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F Elec = E q

F Elec = 150 * 1.6*10^-19

Felec = 2.4*10^-17 N

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Exercise:

Direction is SOUTH  

and

magnetic force F = qv B sin theta

F = 1.6*10^-19 * 2.79 *10^5 * 50.1*10^-6 * sin 90

F = 2.23*10^-18 N

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