A2 Physics |
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Electric Fields and Potentials
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Contents: Electric field lines Coulomb's law Electric field strength, E Electric fields with more than one charge Electric field between parallel plates Electric potential, V Electric potential difference, ΔV Equipotentials and potential gradients Comparing electric and gravity fields |
A plasma ball.
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Electric Field Lines
A positive test charge, Q, at a certain point in an electric field is acted on by a force, F, due to the electric field. Electric fields are defined using positive test charges i.e. a positive point charge is like a 'source' of a field and has lines coming out of it and a negative charge is like the 'sink' of a field with field lines going into it. The fact that charges can be positive or negative makes this force attractive and repulsive. Like charges repel, unlike charges attract (unlike gravity where it is always attractive). As with gravity the test charge in the field needs to be negligible so that it itself produces an insignificant electric field; if it were larger it would effect the resultant electric field and some equations would need to be altered.
Electric field of a positive point charge.
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Electric field of a negative point charge.
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This diagram shows a positive test charge in an electric field. Positive charges move in the direction of the field lines.
Coulomb's Law - A Force Law
The force between 2 charge, Q1 and Q2, at a separation distance, r, is:
This can be simplified by lumping the constants together into one constant, k:
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k = 9.0 x 109 mF^-1 ɛ0 = 8.85 x 10-12 Fm^-1 = permittivity of free space |
Example
Question = What is the force between electrons that are 1m apart?
Answer =
Answer =
Electric Field Strength, E
An electric field is a region where forces act on charges. The electric field strength, E, is the force, F, per unit charge, Q and is measured in NC^-1.
An electric field is a vector field, because it has direction.
Using this equation and substituting the force from Coulomb's law above we arrive at an equation for the electric field strength of a point charge. The electric field strength for a point charge, Q, at a distance, r, from that charge is:
Using this equation and substituting the force from Coulomb's law above we arrive at an equation for the electric field strength of a point charge. The electric field strength for a point charge, Q, at a distance, r, from that charge is:
This equation can be simplified using k to give the following:
Example
Question = What is the electric field strength 1mm away from an electron?
Answer =
Answer =
Electric fields when there is more than one charge...
All you need to do is take one, E1, away from the other, E2, to get a 'resultant' field:
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Two charges, Q1 and Q2, exert forces on a test charge 
In terms of D and x (as shown on the diagram), the equation becomes:
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Example
Question = 2 charges are separated by 30mm. One has a charge of 8nC and the other has a charge of 4nC. Calculate the electric field strength exactly half way inbetween the two charges.
Answer =
Answer =
Electric Field between Parallel PlatesThe voltage, V, is defined as the work done, W, per unit charge, Q:
Work done, W, is calculated by doing the force, F, multiplied by the distance, d, moved in the direction of the force:
Since E=F/Q, then:
And since V=W/Q, we get:
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The electric field strength is therefore also measured in Vm^-1.
Electric Potential, V
The electric potential, V, at a point is the work done per unit positive charge on a positive test charge when moved from a point infinitely far away from any charges to that position. It can also be thought of as the amount of energy it would take to remove a negative charge from a positive field from that point, or, the amount of energy gained by a positive charge when it moves from that point to infinitely far away. Electric potential is a scalar quantity because it is just an amount of energy per charge (it has no direction per se).
The electric potential is measured in Volts or JC^-1. It is the same as the 'voltage' above. The work done to move such a charge is the electric force (from Coulomb's law) x distance it moves, r.
The electric potential is measured in Volts or JC^-1. It is the same as the 'voltage' above. The work done to move such a charge is the electric force (from Coulomb's law) x distance it moves, r.
This then becomes:
The electric potential for an electric field can be positive (unlike in gravity) because we also deal with repulsive forces.
Electric Potential Difference, ΔVThe electric potential difference (ΔV) between two points is numerically equal to the work done (ΔW) in moving a unit positive charge from the point at the lower potential to the point at the higher potential. The work done is independent of the path taken.
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The work done, ΔW, to move a charge, Q, from one potential to another, ΔV, is:
Equipotentials and Potential Gradients
Equipotentials are surfaces (in 3D) or lines (in 2D) connecting points of equal potential. A test charge moving along an equipotential has constant potential energy. No work is done by the electric field.
“The potential gradient (JC-1m-1) in an electric field is the change of potential per unit change of distance in a given direction”.
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Equipotentials are at perpendicular to the electric field lines. In a uniform field the equipotentials are parallel (e.g. in between 2 plates). The electric field strength, E, is equal to the negative of the potential gradient (ΔV/Δr): 
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Comparing Electric and Gravity Fields
