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 anx-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 chargein the figure below?c) What is the total potential energy of this arrangement of charges? Please letU=0 for r+ 10 nC+4 cm-5 nC3 cm-+ Xayis+ 5 nC

Answered: a) Find the direction and magnitude of…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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
+ 10 nC
+
4 cm
-5 nC
3 cm
-+ Xayis
+ 5 nC

Expert Solution

Step 1

To calculate the magnitude and direction of the net electric field, the net electrostatic force on the $- 5 nC$ 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 $- 5 nC$ charge: $E_{n e t}$
The direction of the field: $θ_{E}$
b) The net electrostatic force on the $- 5 nC$ charge: $F_{n e t}$
The direction of the force: $θ_{F}$
c) The total potential energy of the arrangement: $U_{t o t a l}$

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: $k = 9 \times 10^{9} {N.m}^{2} {/C}^{2}$
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:
$E = \frac{k q}{r^{2}}$

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:
$U_{t o t a l} = U_{1} + U_{2} + . . .$

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