Electrostatic potential and equipotentials

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Question statement

A point charge is placed at the origin of a Cartesian co-ordinate system, in vacuum. In this problem we shall use the standard boundary condition for the electrostatic potential from a point charge, i.e. $V(\infty)=0\,\text{V}$ .

When providing numerical answers you may express them using scientific notation. Express values to four significant figures and use the values of physical constants as provided in the course notes.

Give any introductory information the student needs.

			Name	Type	Generated Value

const	number	898774.2437988217
eps0	decimal	dec("0.000000000008854")
q1	number	60
ra	number	26.2488094968
rb	number	28.2842712475
rc	number	26.2488094968
Va	number	2054434.3024195444
Vb	number	1906588.0876378743
Vc	number	2054434.3024195444
x1	number	20
x2	number	17
work	number	127.37492675
q2	number	62
test	decimal	dec("160000")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
(10^(-4))/(4*pi*eps0)

JME function reference

Description

$1/4\pi\varepsilon_0$ and a factor of 10,000 to convert cm and microC to get V in SI units.

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `number`

898774.2437988217

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Parts

Potential at $a$ Gap-fill
1. Gap V_a Number entry
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2. Gap r_a Number entry
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Potential at $b$ Gap-fill
1. Gap V_b Number entry
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2. Gap r_b Number entry
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Potential at $c$ Gap-fill
1. Gap V_c Number entry
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2. Gap r_c Number entry
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Relationship of points Choose one from a list
Energy Gap-fill
1. Gap Energy Number entry
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Ask the student a question, and give any hints about how they should answer this part.

What is the electrostitic potential at the point $a$ , with co-ordinates $x=$ {x1} cm, $y=$ {x2} cm, $z=$ 0 cm for a point charge of {q1} $\mu$ C located at the origin?

$r_a=$ r_a cm.

$V(r_a)=$ V_a Volts.

Advice

Quantiative errors may occur due to unit conversion errors.

A common error is mis-remembering the Coulomb potential which is an inverse distance rule, and not an inverse-square (which is what we see for the electric field in Coulomb's Law). If you squared the distance, revise this section of the course.

The correct formula for the electrostatic potential due to a point charge, taking the boudary condition that $V(\infty)=0$ , is

$\displaystyle V(r)=\frac{q}{4\pi\varepsilon r}$

where $r$ is the distance from the point charge. Note, the electrostatic potential is a scalar field - it does not have a direction.

If you calculated the distance and potential at point $c$ , then you may have not understood the symmetry of the system and the idea that a point charge has spherical equipotentials. Since the distance from the point charge to the points $a$ and $c$ are the same, so is the electrostatic potential.

The potential difference between point $c$ and 'infinity' is obtainable directly from the definition of the potential difference, which is the energy per unit charge. Therefore the energy gained (they are both positive charges so therefore repel) is {q2}×10⁻⁶× $V_c$ .

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This question is used in the following exams:

Tutorial questions - electrostatics by Jon Goss in EEE1001 & PHY1023.
Week 3 tutorial by Jon Goss in EEE1001 & PHY1023.
All electromag by Jon Goss in EEE1001 & PHY1023.
TEST by Jon Goss in Jon's workspace.
E&M digital tutorial week 3 by Jon Goss in EEE1001 & PHY1023.

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Electrostatic potential and equipotentials

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jon Goss 4 years, 3 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`