Point charges, midpoint zero or non zero?

[rcmango]

Homework Statement

Point charges +q and -q are placed at +50 cm and -50 cm on the x-axis, respectively. Is the electric field at the origin (halfway between the charges) zero or nonzero? If nonzero, which direction does it point?

Homework Equations

The Attempt at a Solution

Well I know the charges will be attracting each other because they are opposite in polarity. I'm not sure if the electric field will be zero or non zero. I do know that if the charges were the same polarity, then the midpoint in the middle would both be zero. Please help me figure this one out completely.

 

[NascentOxygen]

Point charges +q and -q are placed at +50 cm and -50 cm on the x-axis, respectively. Is the electric field at the origin (halfway between the charges) zero or nonzero? If nonzero, which direction does it point?

Use the superposition principle. Google "electric field" and "superposition".

 

[kuruman]

Place a positive test charge at the origin. If the net Coulomb force on the test charge is zero, the electric field is zero; if the net Coulomb force is not zero, then the electric field is not zero and point in the same direction as the net Coulomb force.

 

[HallsofIvy]

Homework Statement

Point charges +q and -q are placed at +50 cm and -50 cm on the x-axis, respectively. Is the electric field at the origin (halfway between the charges) zero or nonzero? If nonzero, which direction does it point?

Looking at the +q charge at +50 cm only, a negative charge would feel a force toward it, in the positive direction (and a positive charge in the negative direction). Looking at the -q charge at -50 cm only, a negative charge would feel a force away, in the positive direction (and a postive charge in the positive direction). The two forces add, they do not cancel.

Homework Equations

The Attempt at a Solution

Well I know the charges will be attracting each other because they are opposite in polarity. I'm not sure if the electric field will be zero or non zero. I do know that if the charges were the same polarity, then the midpoint in the middle would both be zero. Please help me figure this one out completely.

 

[rwisz]

The electric field at the origin (halfway between the +q and -q point charges) will be nonzero. This is because the electric field is a vector quantity and the contributions from each charge will not cancel out at the midpoint. The direction of the electric field at the origin will be towards the -q charge, as it has a stronger magnitude compared to the +q charge. This can be seen from Coulomb's law, which states that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the charges. In this case, the distance to the -q charge is smaller, resulting in a stronger electric field towards that direction.