A particle accelerator fires a proton into a region with a magnetic field that points in the +x-direction (a) If the proton is moving in the ty-direction, what is the direction of the magnetic force on the proton? +x-direction -x-direction +y-direction -y-direction +z-direction -z-direction zero force What is the formula used to find the vector magnetic force? What is the right-hand rule for a cross prod (b) If the proton is moving in the -y-direction, what is the direction of the magnetic force on the proton? +x-direction -x-direction +y-direction -y-direction +z-direction -z-direction zero force (c) If the proton is moving in the x-direction, what is the direction of the magnetic force on the proton?

a) -z direction, b) +z direction, c) F=0  

Explanation:

The magnetic force is given by the expression

        F = q v x B

the bold indicate vectors, this equation can be separated in its module

        F = a v B sin θ

and where θ is the angles between the speed and the magnetic field.

The direction of the force can be found with the right-hand rule. For a positive charge, the thumb goes in the direction of speed, the fingers extended in the direction of the magnetic field and the palm points in the direction of the force, if the charge is negative the force is in the opposite direction.

a) Let's apply this to our case

the proton is positively charged

moves in the direction of + x

The magnetized field goes in the direction of y

therefore applying the right hand rule the force must be in the direction of the negative part of the z-axis (-z)

The right-hand rule is used to find this address.

b)  in this case it indicates that the proton moves in the recode of -y

again we apply the right hand rule and the force is in the direction of + z

c)   The proton moves in the x direction

In this case the force is zero because the angle between the field and the speed is zero and the sine is zero, therefore the force is zero

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