Can you show me MATHEMATICALLY how the other components of the electric field for the following problems got canceled? Note: Symmetry argument is not a must here and please show it using Coulomb's Law for calculating the electric field. I just need to see how the components equal to zero.

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Example 1.6 Find the electric field a distance z from the center of a spherical surface of radius R, which carries a uniform charge density o. Example 1.6 Find the electric field a distance z from the center of a spherical surface of radius R, which carries a uniform charge density o.