DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Lecture 3

Chapter 23

Electric field by a continuous charge distribution

PHYSICS II

It’s 8 am. What did I do wrong in my previous life?

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Today we are going to discuss:

Chapter 23:

Section23.3and4:Electric field by a continuous charge distribution Section23.5: The parallel-Plate capacitor Section23.6:Motion of charged particle in an electric field

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Weknowhowtotreatpointcharges.Nowweneedtolearnhowtodeal

withchargescontinuously distributed

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Charge density of a uniformly charged objects

The charge ∆Q in ∆L is:

The linear charge density is:/

Charge Q on a rod of length L Charge Q on a surface of area A

The charge ∆Q in ∆A is:

The surface charge density:/

∆A

Charge Q in volume V

The charge ∆Q in ∆V is:

The volume charge density:/

1D 2D 3DQ

ΔQ

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

A thin ring of radius R is uniformly charged with total charge Q.Find the electric field at a point on the axis of the ring (perpendicular to the ring)

Example Electric field of a charged ring

Example 23.4

ConcepTest Electric Field Lines

Twoprotons,AandB,areinanelectricfield.Whichprotonhasthelargeracceleration?

A) Proton A.

B) Proton B.

C) Both have the sameacceleration.

Stronger field where field lines are closer together.

Weaker field where field lines are farther apart.

E F aF=maF=qE

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Now, let’s find an electric field of a large plate and a capacitor

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Electric field of a disc of chargeThe ring results can be extended to calculate the electric field of a uniformly charged disc.Without derivation:

2 1

In the limit z<<R, it becomes

2El. field created by an infinite charged plate η - surface charge density

Interesting!!! The field strength is independent of the distance z

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

The parallel-plate capacitor

=0Outside the plates

Inside the plates =

It is called a Parallel-plate capacitor

The field inside a parallel-plate capacitor is uniform

Single plates

Let’s bring them very close to each other

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Motionofachargedparticleinanelectricfield.

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

An electron is released from rest at the surface of the negative plate. How long does it take the electron to cross to the positive plate? (Example 23.8)

Example Electron moving parallel to E

DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture3A.Danylov

Thank you