Point charges HELP PLEASE

Question

Two point charges lie on the x axis. A charge of 6.5 uC is at the origin, and a charge of -9.5 uC is at x=10 cm.

a. What is the net electric field at x= -4.0 cm?

b. What is the net electric field at x= +4.0 cm?

Answer 1

So the formula for E from a point charge is k_eQ/d² which is just F_E/q The electric field is the force per positive Coulomb test charge and is a vector. Usually, my approach is to just calculate the magnitude of the field at a point and the direction follows from what you know about a +Q repelling a test charge and a -Q attracting it.

I will do a and leave b for you:

At x = -.04 m Charge 1 is .04 m away E₁ = |8.99 x 10⁹ * 6.5 x 10^-6 C/ (.04 m)²| to the left (repelling a + charge)

At x = .04 m Charge 2 is .14 m away E₂ = |8.99 x 10⁹ * 9.5 x 10^-6 C/ (.14 m)²| to the right(attracting a + charge)

The net E will be E₁ - E₂ to the left (If E₁ was less than E₂ you'd get a negative which implies the E field is to the right)

In (b) the E fields will be in the same direction - so they will add.