Electrical interaction between charged particles can be reformulated using the concept of electric field.
To understand the concept consider the mutual repulsion of two positive charged bodies as shown in fig (a)
Now if remove the body B and label its position as point P as shown in fig (b), the charged body A is said to produce an electric field at that point (and at all other points in its vicinity)
When a body B is placed at point P and experiences force F, we explain it by a point of view that force is exerted on B by the field not by body A itself.
The body A sets up an electric field and the force on body B is exerted by the field due to A.
An electric field is said to exists at a point if a force of electric origin is exerted on a stationary charged (test charge) placed at that point.
If F is the force acting on test charge q placed at a point in an electric field then electric field at that point is E = F/q
or F = qE
Electric field is a vector quantity and since F = qE the direction of E is the direction of F.
Unit of electric field is (N.C^{-1})
Q. Find the dimensions of electric field
Ans. [MLT^{-3}A^{-1}]
7. Calculation of Electric Field
In previous section we studied a method of measuring electric field in which we place a small test charge at the point, measure a force on it and take the ratio of force to the test charge.
Electric field at any point can be calculated using Coulomb's law if both magnitude and positions of all charges contributing to the field are known.
To find the magnitude of electric field at a point P, at a distance r from the point charge q, we imagine a test charge q'to be placed at P. Now we find force on charge q' due to q through Coulomb's law.
$$\boldsymbol{F}=\frac{kqq_{'}}{4\pi \epsilon _{0}r^{2}}
$$
electric field at P is
$$\boldsymbol{E}=\frac{kqq_{'}}{4\pi \epsilon _{0}r^{2}}
$$
The direction of the field is away from the charge q if it is positive
Electric field for either a positive or negative charge in terms of unit vector r directed along line from charge q to point P is
$$\boldsymbol{F}=\frac{kqq_{'}\boldsymbol{\widehat{r}}}{4\pi \epsilon _{0}r^{2}}
$$
r = distance from charge q to point P.
When q is negative , direction of E is towards q, opposite to r.
Electric Field Due To Multiple Charges
Consider the number of point charges q_{1}, q_{2},........... which are at distance r_{1P}, r_{2P},................... from point P as shown in fig
The resultant electric field is the vector sum of individual electric fields as E = E_{1P} + E_{2P} + .....................
This is also a direct result of principle of superposition discussed earlier in case of electric force on a single charge due to system of multiple charges.
E is a vector quantity that varies from one point in space to another point and is determined from the position of square charges.
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