PHYS 241 Recitation Kevin Ralphs Week 2

Overview HW Questions Quiz Continuous Charge Distributions Quiz (Group)

HW Questions Ask Away…

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

Continuous Charge Distributions Motivation for the equation: 𝐸 𝑟 = 𝑞 𝑑𝐸 = 𝑞 𝑘 𝑑𝑞′ 𝑟 − 𝑟 ′ 3 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

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

Quiz Question 4 (Groups) Problem 22-22 p. 758 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?