[Physics] Can electric field be negative

coordinate systemselectric-fieldselectrostaticsforcesVector Fields

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.

Best Answer

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.