# Regarding the Lorentz force:

I know that the Lorentz Force law states that:

$$\vec{F} = q\vec{E}+q\vec{v} \times \vec{B}$$

And then for the magnitude of the force, where $$q_2$$ is the moving charge:

$$E = F/q_2$$, and therefore $$E = kq_1q_2/r^2 * q_2$$, which simplifies to $$E=kq_1/r^2$$

And continuing to find the magnitude, we can replace $$\vec{v}\vec{B}$$ with $$vBsin(\theta)$$

Meaning that the magnitude of the force is:

$$F = kq_1/r^2 + q_2vBsin(\theta)$$

My question is: Is my thought process here correct? Have I arrived at an equation that will accurately describe the magnitude of the force exerted on a moving charge by a magnetic field? If not, what did I do wrong? I'm still trying to get familiar with all of these equations, so anything would help.

• No, that isn't how you add vectors and your last equation is dimensionally incorrect. – Rob Jeffries Sep 2 at 17:54
• @OP -- I am sure you meant $q\vec{v}\times\vec{B}$. – Sayan Mandal Sep 2 at 17:55
• E is not necessarily electrostatic in origin. Your last equation is incorrect. Why are you deriving equations? You should read more until you are in full control of the theory. – my2cts Sep 2 at 19:28
• You can’t understand electromagnetism until you understand vectors, which you normally learn about in a Newtonian mechanics course. – G. Smith Sep 2 at 21:44

No. Firstly the magnetic force is the vector product $$q{\bf v} \times {\bf B}$$ and not the undefined notion "$${\bf v} {\bf B}$$". It's true that $$|{\bf v} \times {\bf B}| = |{\bf V|}|{\bf B}| \sin \theta$$, but the vector $$q {\bf v}\times {\bf B}$$ is perpendicular to both $${\bf v}$$ and $${\bf B}$$. You have not given enough information to know its direction compared to that of $${\bf E}$$ and you need to know all three directions and use vector addition to get the total force. Its magnitude is only the sum of the magnitudes of $$q{\bf v} \times {\bf B}$$ and $$q{\bf E}$$ when the vector $${\bf v} \times {\bf B}$$ is pointing in the same direction as $${\bf E}$$.