Question

1.) What is the Magnitude of the electrostatic force on a +5 C charge 1.75 m to the left of a -2.5 C charge? (show your work)
2.) In What direction does the force on the +5 C charge act?
3.)Calculate the magnitude of the electric field of the -2.5 C charge at the location of the +5 c Charge.
4.) Calculate the magnitude of the total electric field at a point 2m above the +5 C charge. (superposition)
5.) Calculate the magnitude of the electrostatic potential at this point.

Answer 1

1,2). k =9•10⁹ N•m²/C²,
q₁=5 C, q₂= - 2.5 C.
F=k•q₁•|q₂|)/r² =
=9•10⁹•5•2.5/1.75² =3.67•10¹⁰ N (to the right).

3). E=k|q₂|/r² =9•10⁹•2.5/1.75²=
=7.35•10⁹ V/m(to the right).

4). E₁=k q₁/a² = 9•10⁹•5/2²=
=1.125•10¹⁰ V/m,
b=sqrt{2²+1.75²}=2.66 m,
E₂= k|q₂|/b² =
=9•10⁹•2.5/2.66²=3.18•10⁹ V/m.
cosα=2/2.66=0.75,
E=sqrt{E₁²+E₂²-2E₁E₂cosα} =
=sqrt{(1.125•10¹⁰)² +(3.18•10⁹)² -
-2•1.125•10¹⁰•3.18•10⁹•0.75} =
=9.13•10⁹ V/m.
5). φ=φ₁+φ₂ =k q₁/a + k q₂/b =
= k (q₁/a + q₂/b) =
= 9•10⁹(5/2 - 2.5/2.66) =1.4•10¹⁰ V.