My Learning Cart
?
Categories
Account

If the charge density of a spherical charge distribution increases linearly with

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If the charge density of a spherical charge distribution increases linearly with radius, how does the electric field vary inside the sphere?

Options:

  1. Linearly with radius
  2. Quadratically with radius
  3. Inversely with radius
  4. Constant

Correct Answer: Quadratically with radius

Solution: 

The electric field inside a non-uniform charge distribution varies quadratically with radius due to the increasing charge density.

If the charge density of a spherical charge distribution increases linearly with

Practice Questions

Q1
If the charge density of a spherical charge distribution increases linearly with radius, how does the electric field vary inside the sphere?
  1. Linearly with radius
  2. Quadratically with radius
  3. Inversely with radius
  4. Constant

Questions & Step-by-Step Solutions

If the charge density of a spherical charge distribution increases linearly with radius, how does the electric field vary inside the sphere?
  • Step 1: Understand that charge density is how much charge is in a certain volume. In this case, it increases as you move away from the center of the sphere.
  • Step 2: Recognize that the electric field inside a sphere is affected by the charge distribution within it.
  • Step 3: Since the charge density increases linearly with radius, it means that as you go from the center to the surface, there is more charge in the outer layers.
  • Step 4: Use Gauss's Law, which relates the electric field to the charge enclosed within a certain radius.
  • Step 5: Calculate the total charge enclosed within a radius 'r' inside the sphere, which will involve integrating the charge density over the volume.
  • Step 6: Determine how the electric field depends on the total charge enclosed. Since the charge density increases with radius, the total charge will increase more than linearly.
  • Step 7: Conclude that the electric field inside the sphere will vary quadratically with radius because the total charge increases faster than the radius.
  • Electric Field in Non-Uniform Charge Distributions – The relationship between charge density and electric field strength, particularly in spherical charge distributions where charge density varies with radius.
  • Gauss's Law – Application of Gauss's Law to determine the electric field inside a spherical charge distribution.
  • Quadratic Variation of Electric Field – Understanding how the electric field varies as a function of radius when charge density increases linearly.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks