
08262011 #1
Fsc 2nd Year chapter No :1  ELECTROSTATICS
Fsc 2nd Year chapter No :1  ELECTROSTATICS
Topic No :2
FIELDS OF FORCE
Like gravitational fields, electric fields are a field of force that act from a distance, where the force here is exerted by a charged object on another charged object. You may already be familiar with the fact that opposite charges attract, and that like charges repel. Here, we will look at ways to calculate field strengths and the magnitude of forces exerted, in a very similar manner to gravitational fields.Electric field lines are drawn always pointing from positive to negative, like the flow of current. Just like magnetic and gravitational fields, the separation of the lines tell us the relative strength.
Radial fields
Radial fields are drawn from a centre point. The field is stronger nearer the surface of the object, and weakens as you move further away. For a positive charge, the arrows point outwards, and for a negative charge, the arrows point inwards.
The field is directed into a negative point charge...
...and it is directed outwards from a positive one.
Uniform fields
Two plates of opposite polarity (from inside a capacitor) and the lines representing the uniform field between them.
Between two charged plates there is a uniform electric field, which means that its strength is constant between each plate. This is represented by parallel lines, directed from the positive plate to the negative plate. The field curves outwards slightly on the edges of the plates, and it is important that you draw it like that.
Multiple charges
When there are several radial and uniform fields close to each other, they have to be combined into one field, since each of their fields interact and change. The most common shapes are shown, and the arrows, as always, point from positive to negative. You should be able to draw field lines for simple variations on these.
Two point charges of opposite polarity and the lines representing the electric field between them.
A point charge and a plate. Notice how the radial field transitions to a uniform one near the plate.
Coulomb's law
Coulomb's law is very similar to Newton's law of gravitation, except instead of relating the force between two masses together, it relates the force between two charges, Q1 and Q2. Since the two charges are point charges which have radial fields, they follow the inverse square law.
Therefore, the relationship can be expressed as:
. Or, in words:
Any two point charges exert a force on each other that is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Just like Newton's law, we need to introduce a constant of proportionality to make it into an equation, which in this case is k:
. Where .
Permittivity of free space
ε0 is known as the permittivity of free space, and is roughly . It is often useful to just remember that in free space, however you do also need to know , as you may be given the permittivity of different mediums.
Signs of charges
Note that for each charge, you must keep the signs intact in the equation. If you were to have two positive, or two negative charges in the equation, the result would be positive, but if you were to have one negative and one positive charge, the final answer would be negative. The sign of the answer tells us whether the force between the two charges is an attraction, or a repulsion, like charges will repel, and opposite charges will attract. This also explains the minus sign in Newton's law of gravitation, since the force between two masses is always an attraction.
Electric field strength
Just as gravitational field strength is the force exerted per unit mass, we could define the electric field strength in terms of charge:
The electric field strength at a point is the force per unit charge exerted on a positive charge placed at that point.
This is just like saying that the electric field strength is the force a charge of +1 coulomb experiences in that electric field. Therefore, we can find the electric field strength, E, by:
. From this equation, you can see that the electric field strength is measured in NC − 1.
Field strength of a uniform field
You can make a uniform electric field by charging two plates. Increasing the voltage between them will increase the field strength, and moving the plates further apart will decrease the field strength. A simple equation for field strength can be made from these two points:
Where V is the voltage between the plates, and d is the distance between them. Note the minus sign in the equation, which has been added since the force that a positive charge will experience in the field is away from the positively charged plate.
Here you can see that the units of electric field strength is Vm − 1. NC − 1 is equivalent to Vm − 1.
Field strength of a radial field
Since the electric field strength could be said to be the force exerted on a charge of +1C, we can substitute 1 coulomb for Q2 in Coulomb's law. We then get the equation:
, or This will tell us the field strength of a charge, Q, at a distance, r.
Force on particles
To calculate the force an electron experiences in a uniform field, we can combine with in the following steps:
For an electron with a charge of e, this becomes:
, or eE This is useful if you are asked to find the force on an electron in a uniform field, most often in a cathode ray tube.
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