Respuesta :
The magnitude of the total electric charge n terms of q and a is;
E = (4√2)kq/a²
Total Electric Field
The formula for the electric field from a single positive charge is;
E₊ = kq/r²
where;
- k is a constant of proportionality
- q is charge
- r is distance between charges
Since the length of the square is a, then using Pythagoras theorem the length of the diagonal will be a√2.
Half the diagonal will be ¹/₂a√2
Thus putting ¹/₂a√2 for r gives;
E₊ = kq/(¹/₂a√2)²
⇒ E₊ = 2kq/a²
The resultant electric field along the x-axis will be zero because the vectors will cancel each other out while the electric field along the y-axis is;
E_p = 2E₊cos 45°
Thus;
E_p = 2 * 2kq/a² * √2)/2
E_p = (2√2)kq/a²
The magnitude and direction of the resultant field arising from the negative charges is exactly the same and so;
Eₙ = 2E₋ * cos 45°
Solving this gives;
Eₙ = (2√2)kq/a²
Thus;
Total Electric Field is;
E = E_p + Eₙ
E = (2√2)kq/a² + (2√2)kq/a²
E = (4√2)kq/a²
Complete question is;
A point charge is placed at each corner of a square with side length a. All charges have magnitude q. Two of the charges are positive and two are negative. What is the direction of the net electric field at the center of the square due to the four charges, and calculate its magnitude in terms of q and a?
Read more about total electric field at; https://brainly.com/question/9812439
