If the charge density of a non-conducting sphere increases linearly with radius, how does the electric field vary inside the sphere?

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Q: If the charge density of a non-conducting sphere increases linearly with radius, how does the electric field vary inside the sphere?

Solution: The electric field inside a non-conducting sphere with linearly increasing charge density varies linearly with radius.

Steps: 6

Step 1: Understand that the charge density is the amount of charge per unit volume. In this case, it increases linearly with the radius of the sphere.
Step 2: Recognize that inside a non-conducting sphere, the electric field is influenced by the charge contained within a certain radius.
Step 3: Use Gauss's Law, which relates the electric field to the charge enclosed within a Gaussian surface.
Step 4: As the radius increases, the charge density increases, leading to more charge being enclosed within the Gaussian surface.
Step 5: Since the charge density increases linearly, the total charge enclosed also increases in a way that is proportional to the volume of the sphere up to that radius.
Step 6: As a result, the electric field, which depends on the total charge enclosed, will also increase linearly with the radius inside the sphere.