Constants What is the magnitude of the magnetic force on an electron moving in t

Question

Constants What is the magnitude of the magnetic force on an electron moving in the -y-direction at 3.30 km/s A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.70 km/s in the +z direction ex the +y-direction, and an electron moving at 4.70 km/s in the -z-direction experiences a force of 8.60x10-16 N in the +y-direction. periences a force of 2.06x10-16 N in You may want to review (Pages 883-887) Submit For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Magnetic force on a proton Request Answer Part D What is the direction of this the magnetic force? (in the z-plane) from the-c-direction to the -z- direction Submit Request Answer

Explanation / Answer

Would have been a help had you provided the results of the previous parts.

Anyways, we have:

(A)

The z component of the magnetic field is

-2.06x10^(-16)N/(1.602x10(-19)C x 1.70 x 10^3 m/s) = 0.7564 T

The x component of the magnetic field is

8.6 x 10^(-16)N / (1.602x10^(-19)C x 4.70 x 10^3 m/s) = 1.142 T,

but we can't know whether this is positive or negative,

because you didn't say whether the electron is deflected

in the +y direction or the -y direction.

If I assume that the force on the electron also acts in the +y direction,

then the x component of the magnetic field is also positive,

since (-)(-k) x (i) = +j.

I conclude that the magnetic field has magnitude

sqrt(1.142^2 + 0.7564^2) T = 1.37 T

(B)

and its direction is in the x-z plane at

arctan (0.7564/1.142) = 33.52 degrees away from the + x-axis

and 56.48 degrees away from the + z-axis.

(C)

In doing this part, I will again assume that the electron moving in the -z direction

was deflected in the +y direction.

F = qv x B

= (-1.602 x 10^(-19)C)(-3.3 x 10^3 m/s j) x (1.142 i + 0.7564 k) T

= (-6.037 k + 3.999 i) x 10^(-16) N

The magnitude of this force is

sqrt(6.037^2+3.999^2) x 10^(-16) N = 7.24 x 10^(-16) N

(D)

and its direction is in the x-z plane,

perpendicular to the magnetic field,

so 33.52 degrees away from the negative z axis

and 56.48 degrees away from the positive x axis.

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