Three point charges of +2q, -q and -q are placed at the corners A, B and C of an equilateral triangle ABC of side ‘x’.
To find the net electric field at a specific point due to multiple charges, we need to calculate the electric field created by each charge individually and then vectorially add them. The electric field created at a point by a point charge is given by Coulomb's law.
Coulomb's law states that the electric field created by a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the point charge and the point where the electric field is being measured.
The formula for the electric field created by a point charge is:
E = k * (q / r^2)
Where:
- E is the electric field
- k is Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2)
- q is the magnitude of the charge
- r is the distance between the point charge and the point where the electric field is being measured
Now let's calculate the electric field created by each charge at a point P, and then sum them up vectorially to find the net electric field.
1. Electric field due to the +2q charge (at point A):
The distance between point A and point P is equal to the length of one side of the equilateral triangle, which is 'x'. Therefore, r = x.
The magnitude of the electric field created by the +2q charge at point P is given by:
E1 = k * (2q / x^2)
2. Electric field due to the -q charge (at point B):
The distance between point B and point P is also 'x'.
The magnitude of the electric field created by the -q charge at point P is given by:
E2 = k * (q / x^2)
3. Electric field due to the -q charge (at point C):
The distance between point C and point P is also 'x'.
The magnitude of the electric field created by the -q charge at point P is given by:
E3 = k * (q / x^2)
Now, to find the net electric field at point P, we need to add these electric fields vectorially. Since the charges are placed at the corners of an equilateral triangle, the direction of each electric field is along the line connecting the charge to point P.
To add the electric fields vectorially, consider the magnitude and direction of each electric field. The electric fields due to the -q charges will have the same magnitude but opposite direction. Hence, their vector sum will be zero.
The net electric field at point P is the vector sum of the electric field due to the +2q charge and the electric fields due to the -q charges.
Net electric field (E_net) at point P = E1 + E2
Now, you can substitute the expressions for E1 and E2 into the equation and simplify it to find the net electric field at point P.