# Can electric field be negative?

According to the equation , $$E = kQ/r^2$$

If the source charge is negative electric field produced by the charge must also be negative. My teacher said electric field can never be negative, it'll either be positive or zero. Online sources pointed out that since electric field is a vector when doing calculation we only report the magnitude.

Another doubt was with electrostatic force is,why is it always positive? According to columb's law force is directly proportional to modulus of product of charges. Can't it be negative like attractive and repulsive forces.

The electric field is a vector quantity. For the vector ${\bf v}$ you can write this as $|{\bf v}|$ multiplied by a unit vector, say ${\bf n}$, that is $${\bf v} = |\bf{ v}| {\bf n}.$$

It is conventional to take the magnitude as a positive number, but if you take it as a negative number you can write $${\bf v} = -|\bf{ v}| (-{\bf n})$$ and the field points in the opposite direction.

• Is electrostatic force always positive, well it is according to columb's law. Or as it is written in the other answer it can be effectively represented by a unit vector? – susan J Mar 6 '18 at 12:55

Try to ask yourself the question: what does it mean that anything is "negative"? The term "negative" has no physical meaning in itself before we define it to mean something.

• How does a negative number (scalar) make physical sense? What does $-2\;\mathrm{kg}$ or $-10\;\mathrm{apples}$ mean? We can choose to understand it as the loss of an amount when it fits the context.

• How does a negative arrow (vector) make physical sense? What does $-\vec F$ or $-\vec v$ or $-\vec E$ mean? We can choose to define it as the opposite of the vector, meaning the same vector in the opposite direction.

And so, a negative vector - or more precisely: the negative of a vector - has been defined to mean: The same vector in the opposite direction.

Now that we have a chosen definition, we can use any vector quantity with signs. Forces, velocities and also fields, including electric fields, are represented by vectors. A negative electric field just means: a field pointing/pushing opposite to what a positive field would do.

• About the last sentence: then what is a positive field? – lalala Jun 8 at 3:42
• @lalala That depends on the context, on the type of field. In the case of electric fields, the positive field direction is always along with the direction it pushes a positive electric charge. By definition. – Steeven Jun 8 at 6:05
• I know what a positivd direction is. But this doesnt define positive field. Also how would you distinguish this from the 'negative" field. To be explicit: the fiel Ez=1 all othe componentd 0. Is this a positive or negative field? – lalala Jun 8 at 7:03
• @lalala The point of my answer is that the notion of "negative" just means "opposite", so to say, in this case. There is no such thing as a negative field - it doesn't make physical sense. We still say it now and then, and when we say it, what we imply is that a negative field is a field where the direction at every point is opposite to that of a positive field, whatever that positive field is. Defining a positive field is a bigger task. But having that, defining a negative field is easy: it is just the same field but pointing opposite at every point. – Steeven Jun 10 at 10:16

Electric Field can never be negative . As electric field is Force experienced by charge divided by magnitude of charge . So in magnitude , we take mod of charge. So even in case if charge is negative , then due to mod it becomes positive . Hence Electric Field also becomes positive . So , electric field is always positive .