four equal point charges are at the corners of a square. where besides infinity and at the center of the square is the strengh field zero?
Nowhere else.
To determine the points where the electric field strength is zero, we need to consider the interactions between the four point charges. Let's assign some labels to the charges for easier reference: A, B, C, and D. Considering the symmetry of the square, we assume that all charges are identical (having the same magnitude).
To find the locations other than infinity and the center of the square where the electric field strength is zero, we can analyze the forces on a test charge placed at different positions.
1. At the center of the square:
Since the charges are placed at the corners of the square and are equidistant from the center, the electric field vectors from each charge will have the same magnitude and direction, resulting in a zero net force on the test charge. Therefore, the electric field strength is zero at the center of the square.
2. At infinity:
As we move far away from the charges (towards infinity), the electric field strength from each charge decreases. Eventually, at a large enough distance, the combined effect of all charges becomes negligible, resulting in an electric field strength approaching zero.
3. Along the diagonals:
Consider a point along one of the diagonals of the square. We can analyze the forces on the test charge from the charges at the corners.
Assume that the charges A and C are positive, and B and D are negative. As the test charge moves along the diagonal away from the center, the forces from charges A and C repel it, while charges B and D attract it. The electric field vectors will cancel each other at some point along the diagonal, resulting in a net force of zero and zero electric field strength.
4. Midway between the charges:
Now, consider the midpoint of a side of the square. At these points, we can look at the forces acting on the test charge from adjacent corner charges only. For example, if we consider the midpoint between A and B charges, the force from A will attract the test charge, while the force from B will repel it. By carefully adjusting the magnitudes of the charges, it's possible to find a point where these forces cancel each other, resulting in zero electric field strength.
In summary, besides infinity and the center of the square, there are points along the diagonals and the midpoints between charges where the electric field strength is zero. The exact location of these points would depend on the specific geometry and magnitudes of the charges.