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The concept of a field was developed by Michael Faraday. An electric field intensity or simply, electric field is said to exist in the region of space around a charged object. When another charged object, (the test charge) enters this space, we say the test charge experiences an electric force, F_{e }due to this field.
Definition: We define the electric field due to the source charge at the location of the test charge to be the electric force on the test charge per unit charge.
In simple words, Electrostatic force per unit positive test charge is defined as Electric Field due to the source charge.
is a vector quantity and its direction is same as that of force on the test charge. The unit and dimensions for Electric Field would be Newton/Coulomb and [M^{1} L^{1} T^{3}I^{1}] respectively.
Note: The electric field is the property of its source. Presence of test charge is not necessary for the Electric field (due to source charge) to exist. It exists with or without the test charge. The test charge is used to detect and measure the Electric field due to source charge.
Note: Observe the figure, we say that the ‘source’ charge + Q has created a region of influence around the space itself. This region of influence is visualized by defining the concept of Electric Field.
Now, if we bring any charge in this region, by Coulomb’s law, it will experience an electrostatic force. Now, the question arises, How do these charges realise that the other charge has come in its ‘territory’ or ‘region of influence’?
It happens because the other charge or ‘the test charge’ interacts with the Electric Field of the source charge and thus, electrostatic force is exerted on each other.
Conventionally, we only take the test charge to be positive. Therefore, a positive source charge would repel a ‘positive test charge’ and a negative source charge would attract a ‘positive test charge’. Thus, the electric field can be visualized in space as following:The direction of electric field is radially outwards for a positive charge and is radially inwards for a negative charge as shown in the figure above based on the direction of electrostatic force on ‘positive test charge’.
There are some points to always to be kept in mind. These are
1. It is important to note that with every charged particle, there is an electric field associated which extends up to infinity.
2. No charged particle experiences force due to its own electric field.
As discussed earlier, if we find the electric field due to a point charge at a distance r from it. Its magnitude can be given as
By definition,
Electrostatic force on test charge +q,
Now,
Note: That if the source charge is negative i.e. –Q then we can visualise the electric field by
This means, we can simply reverse the Electric field vector’s direction.
Thus, Electric Field due to a point charge of magnitude + Q at a distance r from it is given by the expression KQ/r^{2} and its direction is along the line joining the source charge and the point of consideration.
Q. Why have we defined the concept of electric field? Is it really necessary? If eventually, we are measuring the electrostatic force, why can’t we do it directly using Coulomb’s Force?
Ans.
Remember, this diagram, it represent electric field or the ‘region of influence’ of charge +q around the space. Now, the arrows in this diagram are called the electric field lines. Without these lines, we would not be able to visualize the concept of electric field. In this figure, each arrow indicates the electric field, i.e., the force acting on a unit positive charge, placed at the tail of that arrow. Connect the arrows pointing in one direction and the resulting figure represents a field line. We thus get many field lines, all pointing outwards from the positive point charge.
Note: That electric field lines of +2Q charge are twice in number than that of +Q. So, irrespective of the number of lines in each representation, the ratio must be maintained to 2.
Relative density of field lines at distance r/Relative density of field lines at distance 2r = 4/1
Similarly,
Relative density of field lines at distance 2r/Relative density of field lines at distance 3r = 9/4
Note: That the red dots represent positive charge and the blue dots represent the negative charge and try to verify all the properties of electric field lines listed above.
(a) Electric field versus x for a positive point charge kept at the origin. Note that the electric field at positive x is positive, because it is in positive direction. At negative x it is negative, because it is in negative direction.
(b) Electric field versus x for a negative point charge kept at the origin. Note that the electric field at positive x is negative, because it is in negative direction. At negative x it is positive, because it is in positive direction.
Ans. Before calculating, let us physically see the location of the point where the electric field can be zero. At points other than the x axis, say above the xaxis, both the charges will have a component of the electric field in the positive direction. This y component of the electric field does not cancel out. So the net electric field at that point will not be zero. The same statement also holds true for points which are not in xy plane.
On the xaxis also we can see that on the points beyond x = 6 m and points on the negative x axis, both the electric fields will be in the same direction. So the net electric field cannot be zero. At some point between the two charges, the electric field due to both of them will be in opposite direction. So the electric field will be zero at a point between x = 0 and x = 6m.
Let the x coordinate of neutral point (E = 0) be x,
Therefore,
By solving above equation for x, we get x = 2m.
Hence, at x = 2 between these two charged particles, there exists a point where net electric field due is zero i.e. neutral point.
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