ABC is an equilateral triangle of side 0.1m. Point charges of +3nC and -3nC are placed at the corners A & B respectively. Calculate the resultant electric field at C
To calculate the resultant electric field at point C due to the charges at points A and B, we can use the principle of superposition. According to this principle, the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.
Step 1: Calculate the electric field due to the +3nC charge at point A
The electric field at a point due to a point charge can be calculated using Coulomb's Law. The formula to calculate the electric field (E) is:
E = k * (q / r^2)
where:
- E is the electric field
- k is the electrostatic constant (9 × 10^9 Nm^2/C^2)
- q is the magnitude of the charge
- r is the distance between the charge and the point where the electric field is being calculated
In this case, the magnitude of the charge (q) is +3nC (3 × 10^-9 C), and the distance (r) between the charge A and point C is equal to the length of one side of the equilateral triangle (0.1m). Hence, we can calculate the electric field at point C due to the charge at point A.
Step 2: Calculate the electric field due to the -3nC charge at point B
Similarly, we can calculate the electric field at point C due to the charge at point B using Coulomb's Law.
Step 3: Calculate the resultant electric field at C
The resultant electric field at point C can be found by vector sum of the electric fields due to charges at A and B. Since the charges are on the corners of an equilateral triangle, the angles between the lines joining the charges to point C are all 60 degrees.
Finally, calculate the resultant electric field E_total using the formula:
E_total = sqrt((E_A^2) + (E_B^2) + (2 * E_A * E_B * cosθ))
where:
- E_A is the electric field at C due to charge A
- E_B is the electric field at C due to charge B
- θ is the angle between the lines joining the charges to point C (which is 60 degrees in this case)
Now, substitute the calculated values of E_A, E_B, and θ into the formula to find the resulting electric field at point C.
ok ok
Q at A and Q at B
add components along axis of altitude of triangle from A B
E along axis = (k 3nC cos 30 - k 3nC cos 30)/.1^2
which is zero
E perpendicular to that axis, in other words parallel to AB is
E = (k 3nC sin30 + k 3nC sin 30)/.1^2
= k *2*.5 *3nC /.01
= 100 k *3nC