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A proton moves in the +z direction through a uniform magnetic field that points in the...

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A proton moves in the +z direction through a uniform magnetic field that points in the -y direction and has a magnitude of 2.5 T. If the proton...

moves with a speed of 5.7 x 10^6 m/s through this field, what is the STRENGTH AND DIRECTION of the force that acts on a proton. 

And how would you go about finding the direction? I'm kind of confused on the right hand rule. Thanks for your help :)

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The lorentz force on a charged particle is


where F is the force, q is the particles charge, E is the electric field, v is the particles velocity and B is the magnetic field, whilst x denotes the cross product of the two vectors v and B.

As there is no electric field, the lorentz force equation becomes just


The vector B, the magnetic field, is pointing in the negative y direction, thus its vector is


The vector v, the particle's velocity, points in the positive z direction, thus its vector is

v=(0,0,5.7x10^6 m/s)

To find the direction and magnitude of the force, you need to calculate the cross product of v and B. The way the cross product is calculated is


By following this calculation, you get that the only non-zero component of the force vector is


whilst the y and z components are both zero. This means that the vector describing the force is


Its magnitude is 2.32x10^-12N and its direction is in the positive x direction.


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