Direction of electric force and magnetic force Lorentz force

[going2breakdown]

I have a question here asking about a particle with a charge moving through a uniform electric field and a uniform magnetic field. It asks for the total electromagnetic force on the particle. Apparently you just add the two forces. What is confusing me is that the magnetic force will always point towards the center. That isn't the same with the electric force, so how is it I can just add the two forces together to get the "Lorentz force"

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[anon4895]

I have a question here asking about a particle with a charge moving through a uniform electric field and a uniform magnetic field. It asks for the total electromagnetic force on the particle. Apparently you just add the two forces. What is confusing me is that the magnetic force will always point towards the center. That isn't the same with the electric force, so how is it I can just add the two forces together to get the "Lorentz force"

You have to add them together as vectors, since forces are vectors. However when the forces are acting in the same direction then vector addition is really just addition.

Imagine you have a positively charged particle moving up and your magnetic field is pointing into the page. The force acts to the left. Now imagine the electric field is pointing to the left, the force from this also points to the left. This means you can just add them together. Most problems will have the electric and magnetic fields positioned in such a way that the forces from both fields point in the same direction. If this is not the case then yeah you can't just add them together.

 

[going2breakdown]

Oh! They mean the instantaneous force on the particle when they point in the same direction, before the curved trajectory changes the force vector direction. Funny, you'd think they'd mention that...unbelievable. This saved me from a lot of worry, thanks.