In: Physics
When you calculate the net electric field in a location due to
the presence of more than one large charge (Q), it is generally not
helpful to include the sign of the charges in the
equation for electric field. Why not? Specifically, what does the
sign of a charge tell you about the direction of the electric
field, and what does the sign of a charge NOT tell you
about the direction of the electric field?
Electric field is a vector quantity , so it will have magnitude as well as direction,
When there is a single charge and we have to calculate the direction of electric field at any point P due to given charge, we can easily calculate the direction of electric field with the help of sign of charge as when there will be negative sign, then direction of electric field will be towards the negative charge on the line joining charge Q snd point P and when there will be positive charge then direction of charge at point P will be away from the charge on the line joining charge Q and point P and we dont have to put sign to the electric field to indicate direction.
Similary when there will be more than one charges i.e. system of more than one individual charge then the magnitude of electric field at point P due to individual charges along with direction are shown on the basis of sign of charge as stated above without putting any sign in the electric field equation, and finally total net electric field is calculated by vectorial addition of individual electric fields along with their directions. Hence we dont require to include any sign in the equation of electric field.