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Four equal positive charges are fixed at the vertices of a square of side L. Z-axis is perpendicular to the plane of the square. The point z = 0 is the point where the diagonals of the square intersect each other. The plot of electric field due to the four charges, as one moves on the z-axis.?
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Four equal positive charges are fixed at the vertices of a square of s...
Electric Field Due to Four Charges in a Square


Setup


  • Four equal positive charges are fixed at the vertices of a square of side L.

  • Z-axis is perpendicular to the plane of the square.

  • The point z = 0 is the point where the diagonals of the square intersect each other.



Electric Field


  • The electric field due to the four charges is given by the vector sum of the electric fields due to each charge.

  • Since the charges are fixed, the electric field at any point on the z-axis depends only on the distance of that point from the plane of the square.

  • The electric field due to each charge is directed radially away from the charge.

  • At z = 0, the electric field due to opposite charges cancel out each other and the resultant electric field is zero.

  • As one moves away from z = 0, the electric field due to the charges becomes non-zero and varies in magnitude and direction.

  • The electric field is maximum at points equidistant from the four charges on the z-axis.

  • As one moves further away from these points, the electric field due to opposite charges cancel out each other and the resultant electric field decreases.



Plot of Electric Field


  • The plot of electric field due to the four charges as one moves on the z-axis is a symmetric plot.

  • The plot has maxima at points equidistant from the four charges on the z-axis.

  • The maxima form a square pattern on the z-axis.

  • The electric field at the center of the square (z = L/2) is maximum.

  • The electric field at the corners of the square (z = √2L/2) is minimum.

  • The electric field is zero at z = 0, z = ±L, and z = ±√2L/2.

  • The magnitude of the electric field decreases as one moves away from the center of the square on the z-axis.

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Four equal positive charges are fixed at the vertices of a square of side L. Z-axis is perpendicular to the plane of the square. The point z = 0 is the point where the diagonals of the square intersect each other. The plot of electric field due to the four charges, as one moves on the z-axis.?
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