# Question #7d64a

Jun 15, 2016

I think it is a matter of convention and how force equation is stated.

#### Explanation:

Recall that the Force $\vec{F}$ experienced by a charged particle of charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the relation
$\vec{F} = q \left(\vec{v} \times \vec{B}\right)$
We also know that
velocity $\vec{v} = \text{displacememt"/"time}$
If the charge moves through distance $=$length $\vec{L}$ in time $t$
$\vec{v} = \frac{\vec{L}}{t}$. Inserting in the force equation we obtain
$\vec{F} = q \left(\frac{\vec{L}}{t} \times \vec{B}\right)$
Rearranging scalar quantities we get
$\vec{F} = \frac{q}{t} \left(\vec{L} \times \vec{B}\right)$
$\implies \vec{F} = I \left(\vec{L} \times \vec{B}\right)$, where $\frac{q}{t} = I$ is the current flowing in the wire.

You may use the expression $\vec{F} = | \vec{L} | \left(\vec{I} \times \vec{B}\right)$ knowing well that the direction of $\vec{I} \mathmr{and} \vec{L}$ is same.
However, we must appreciate that direction of $\vec{L}$ defines the direction of $\vec{I}$. Perhaps and not vice versa.