If the radius of a spherical Gaussian surface is doubled, how does the electric field due to a point charge at its center change?

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Q: If the radius of a spherical Gaussian surface is doubled, how does the electric field due to a point charge at its center change?

Solution: The electric field due to a point charge is independent of the radius of the Gaussian surface; it remains the same.

Steps: 6

Step 1: Understand what a point charge is. A point charge is a charged particle that is very small compared to the distance from it to other objects.
Step 2: Know what a spherical Gaussian surface is. It is an imaginary sphere used in physics to help calculate electric fields.
Step 3: Remember that the electric field (E) created by a point charge depends only on the amount of charge (Q) and the distance (r) from the charge, according to the formula E = k * Q / r^2, where k is a constant.
Step 4: Realize that when you double the radius of the Gaussian surface, you are changing the distance (r) from the charge to the surface, but not the charge itself.
Step 5: Understand that the electric field at the surface of the Gaussian sphere is still determined by the charge at the center, not the size of the sphere.
Step 6: Conclude that even if the radius of the Gaussian surface is doubled, the electric field due to the point charge at its center remains the same.