1. PHYS 241 Recitation
Kevin Ralphs
Week 2

2. Overview HW Questions Quiz Continuous Charge Distributions
Quiz (Group)

3. HW Questions
Ask Away…

4. Continuous Charge Distributions
This week’s material is largely a lesson in calculus
Difficulties in predicting the field due to a continuous charge distribution:
The distribution may have an odd shape
The charge density may change through the distribution
This suggests an approach via calculus is appropriate

5. Continuous Charge Distributions
Motivation for the equation:
𝐸 𝑟 = 𝑞 𝑑𝐸 = 𝑞 𝑘 𝑑𝑞′ 𝑟 − 𝑟 ′ 𝑟 − 𝑟 ′
Very far from a charge distribution, it looks like a point charge
So if we “chop” up the distribution into small enough pieces, each one will have a field contribution we can calculate
The principle of superposition then allows the integrand to approach the true field

6. Continuous Charge Distributions
General procedure to setup the integrals
Write the general integral down
Draw a diagram and label all the parts of the integral
Change integral to integrate over where the charge lies (aka parameterization)
Identify elements of the integrand that depend on the integrating variable
Determine explicit relationships with the integrating variable
Integrate

7. Quiz Question 4 (Groups)
Problem p A ring of radius a has a charge distribution on it that varies as λ = λo sin(θ). (a) What is the direction of the electric field at the center of the ring? (b) What is the magnitude of the field at the center of the ring?