# Direction of electric field and force

my physics textbook, "Giancoli...", stated this

If $q$ is positive, [the force and electric field] point in the same direction. If $q$ is negative, [the force and electric field] point in opposite directions.

But in a previous paragraph, it had also stated:

We see that the electric field at any point in space is a vector whose direction is the direction of the force on a tiny positive test charge at that point, and whose magnitude is the force per unit charge

If the electric field is in the direction of the force on the positive test charge, why would the force and electric field be in opposite directions if $q$ is negative?

Picture if more context is needed:

The given equation $\vec E=\frac{\vec F}q$ can be easily rearranged to $\vec F=\vec Eq$.

When the charge $q$ is positive then the direction of $\vec F$ is the same as the direction of $\vec E$ - all values are positive.

When the charge $q$ is negative (i.e. $-q$) then $\vec F$ will be negative: $\vec F=\vec Eq \Rightarrow -\vec F=\vec E(-q)$.

This is similar to the attraction of charges $F=\frac{kq_1q_2}{r^2}$ where, if $q_1$ and $q_2$ both have the same sign (both positive or both negative) then $F$ is positive and the charges repel each other, whereas if $q_1$ and $q_2$ have opposite signs (one positive and one negative) then $F$ is negative and the charges are attracted to each other.

But instead of two charges, you have one charge and an electric field. If you consider the electric field to be originating from a positive charge ($+q$) then the direction of the field is away from that (imaginary) charge and the direction of force exerted on another positive charge in the field is in the same direction as the field - the source of the field repels the positive charge, but the direction of force exerted on a negative charge in the field is instead in the opposite direction to the field - the source of the field attracts the negative charge.

• thanks for the explanation and clearly stating the charge in your example. The book the didn't clearly state the charges responsible for what and i got lost. thanks again! – Harmony Jan 25 '18 at 2:23

This is Coulomb's Law. Like charges repel. Opposites attract. Just think it through.

The field is just there. The sense of the field. That is to say, positive or negative "direction", is an accident of history. Put a positive charge in the field and the force pushes one way. Put a negative charge in, and the force pushes in the negative of that direction.

Other answers already suffice the needs of the question. If there is still some ambiguity, just remember that The Electric field experienced by the test charge, q, is independent of q.

So it always points in the same direction for same distribution of source charge, Q, even if nature of q's change.

Now the force due to the same field acts in different direction. A positive experiences force in the direction of the field, whereas negative charge opposite to the field, i.e. in towards the source charge or in towards the increasing field.

Because a positive and a negative charge move opposite!

An electric field is created by some charge - that charge could be positive.

• Placing a positive test charge nearby will cause it to be repelled (equal charge-signs repel).
• Placing a negative test charge nearby will cause it to be attracted (different charge-signs attract).

They experience the exact same electric force, just in opposite directions. An electric field that pushes in a charge will pull in the opposite charge.

So, the electric force obviously has a direction. People then invented a direction for the field itself and said that it doesn't matter what we choose, so let's just choose its direction to be equal to the electric force in a positive charge. Therefore the field and force are always pointing the same way at a positive charge and opposite at a negative charge. It is pure convention.

• thanks. I hope there aren't more "conventions" in electromagnetism sweats. – Harmony Jan 25 '18 at 2:16