# Magnetic Force and Speed

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#### G1SG2

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I remember a TPR question asking about what a magnetic force can do and it said that the magnetic force cannot change the speed of a particle? Is this true? I don't understand how that can be true since any force (or net force) can cause an acceleration, which can change the speed of a particle? I know the answers said something like the magnetic force can be generated by a moving charge, can accelerate a moving charge, and can exert a force on a moving charge, but not change the magnitude of the speed of the charge (only change its direction)? Why?

#### matth87

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Mathmatical Definition for acceleration

a = (delta)v / time

V = velocity, which is a vector, magnitude and direction
Speed = scalar that is just magnitude

You can still have an acceleration by just changing the direction and not affecting the magnitude.

When forces are applied perpendicular to velocity you will have a change in direction but no change in speed.

Its just like centripetal acceleration. V points tangent to the circle. Fc points inward. You do not change the magnitude of V, just the direction.

In order for acceleration to affect the speed it MUST have a component of the vector point in the same or opposite direction.

#### G1SG2

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Mathmatical Definition for acceleration

a = (delta)v / time

V = velocity, which is a vector, magnitude and direction
Speed = scalar that is just magnitude

You can still have an acceleration by just changing the direction and not affecting the magnitude.

When forces are applied perpendicular to velocity you will have a change in direction but no change in speed.

Its just like centripetal acceleration. V points tangent to the circle. Fc points inward. You do not change the magnitude of V, just the direction.

In order for acceleration to affect the speed it MUST have a component of the vector point in the same or opposite direction.

No I know that you can have acceleration just by changing direction as in UCM, but my question is, why can't the magnetic force change the speed of a particle at all?

#### G1SG2

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OH nevermind-I just remembered that since the force is always perpendicular to the particle's velocity, it can do no work, and by the work-energy theorem, can't change it's KE.

#### G1SG2

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Wait, but in TBR, the first passage in the electricity/magnetism section (question 2) says that the work done on an electron in moving it across the bar is w=q*v. I thought the magnetic field does no work since the force is perpendicular to the displacement???? #### amine2086

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A charged particle accelerates in a magnetic field. The direction of the acceleration depends on the direction of the force and the charge (+/-) of the particle. So I am not sure why TPR is claiming magnetic force can not change the speed of the particle as change in acceleration is change in velocity. This must be one of the typos or something.

#### Seraph 84

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You won't change the speed, but you will change the direction. This is why particles are deflected when moving perpendicular to a magnetic field. A little short on the explanation.

#### G1SG2

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A charged particle accelerates in a magnetic field. The direction of the acceleration depends on the direction of the force and the charge (+/-) of the particle. So I am not sure why TPR is claiming magnetic force can not change the speed of the particle as change in acceleration is change in velocity. This must be one of the typos or something.

I mixed up the electric and magnetic fields, q*V is the work done by the electric field. The magnetic field cannot change the velocity of the particle, as the force is perpendicular to the velocity of the particle, and so it cannot do work, and by the work-energy theorem, cannot change the KE and thus the speed of the particle. The acceleration refers to the change in direction, as a particle moving in a uniform magnetic field moves in a circular motion, although at constant speed.

#### destroythemcat

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Anyone want to re-explain this