Question

PROBLEM 1 (15 points) Two charges, of magnitude q ( >0) are placed on the r axis of a Cartesian coordinate system, at positions x- -L and x- L respectively (A) Find the electric field at positions x =-L/2, x = 0, and x = L/2 on the x axis by using Coulomb's law and the superposition principle. Represent graphically the field vectors at these positions (B) Can the electric field at 0 be predicted based on a symmetry argument? Explain your reasoning If the field at x = L/2 is known, can the field at x =-L/2 be predicted based on a symmetry argument? Explain your reasoning.

Answer 1

Part (A). Taking direction of electric field toward +ve x axis as +ve direction and toward negative x axis as negative direction.

Part(B). Yes ,we can predict electric field at x= 0 based on symmetry argument.

due to left charge electric field direction at x=0 is toward +ve x axis.

And due to right charge electric field direction at x=0 is toward -ve x axis.

And electric field due to both charge is equal and opposite in magnitude and direction.adding both of them we get electric field at x=0.

Similarly we can also find at x= +L/2 by using symmetry.