a) Find the direction and magnitude of the net electric field vector created by the +10 nC and +5 nC charges at the location of the -5 nC charge. Please define an x-axis and give an angle clockwise/counterclockwise with respect to this axis. b) What is the direction and magnitude of the force vector F on the -5 nC charge in the figure below? c) What is the total potential energy of this arrangement of charges? Please let U=0 for r

To calculate the magnitude and direction of the net electric field, the net electrostatic force on the $-5 \text{nC}$ charge and the potential energy of the arrangement.

Given:
The figure:

To calculate:
a) The magnitude of the net electric field at the location of the $-5 \text{nC}$ charge: $E_{net}$
      The direction of the field: ${\theta }_E$
b) The net electrostatic force on the $-5 \text{nC}$ charge: $F_{net}$
      The direction of the force: ${\theta }_F$
c) The total potential energy of the arrangement: $U_{total}$

The electrostatic force between two charges is given by Coulomb's Law:
$F=\frac{k{q}_1{q}_2}{r^2}$
where,
$q_1$ and $q_2$ are the two charges,
$r$ is the distance between the charges, and
$k$ is Coulomb's constant. The value is: $k=9\times {10}^9 {\text{N.m}}^2{\text{/C}}^2$
A negative force indicates that the force is attractive, a positive force indicates that the force is repulsive.

The electric field at a location due to a charge is given by the formula:
$E=\frac{kq}{r^2}$

The potential energy between two charges is given by the formula:
$U=\frac{k{q}_1{q}_2}{r}$
When multiple charges are brought into a charge configuration, the potential energies are added:
$U_{total}=U_1+U_2+...$