# Question on the Lorentz force: Why is the force not F=q(v×B) = F=qv×qB

• I
unplebeian
TL;DR Summary
Why is the charge not multiplied to the cross product
Background:
is the equation of Lorentz force for the force acting on a moving charge in electric and magnetic field.

For the magnetic field only it is : F=qv×B.

Question:
For magnetic field only why is the force not F=q(v×B) = F=qv×qB

Last edited by a moderator:

Gold Member
MHB
TL;DR Summary: Why is the charge not multiplied to the cross product

Background:
is the equation of Lorentz force for the force acting on a moving charge in electric and magnetic field.

For the magnetic field only it is : F=qv×B.

Question:
For magnetic field only why is the force not F=q(v×B) = F=qv×qB
You are only multiplying by q once, so
##q \textbf{v} \times \textbf{B}##

##= q ( \textbf{v} \times \textbf{B} )##

## = (q \textbf{v} ) \times \textbf{B}##

##= \textbf{v} \times (q \textbf{B})##

-Dan

Ibix
unplebeian
Hi, Dan,
I'm sorry I didn't get it. That is a scalar multiplication so q should be multiplied to both. Generally a(bxc)= abxac.
Why are we multiplying only once?

Homework Helper
Gold Member
2022 Award
Generally a(bxc)= abxac.
This is wrong.
$$a(\mathbf b \times \mathbf c) = a\mathbf b \times \mathbf c = \mathbf b \times a\mathbf c$$You must be thinking of:
$$a(\mathbf b + \mathbf c) = a\mathbf b + a\mathbf c$$

Gold Member
MHB
Hi, Dan,
I'm sorry I didn't get it. That is a scalar multiplication so q should be multiplied to both. Generally a(bxc)= abxac.
Why are we multiplying only once?
Is ##2(3 \times 4 ) = (2 \cdot 3) \times (2 \cdot 4)##?

-Dan

$$a(\mathbf b \times \mathbf c) = a\mathbf b \times \mathbf c = \mathbf b \times a\mathbf c$$You must be thinking of:
$$a(\mathbf b + \mathbf c) = a\mathbf b + a\mathbf c$$