Outline

• Area vector

• Vector flux

• More problems

• Solid angle

• Proof of Gauss’s Law

The flux of E

SdEd

S

s SdE

SdE

More on area vector ….

n

Suppose there was an electric field given by

.0 xiEE

What would be the electric flux through a plane with area A if the plane were oriented in the y-z plane at ?0xx

What would be the electric flux if the plane were oriented in the x-z plane at ?0yy

Suppose there was an electric field given by

yiEE

0

What would be the electric flux through a plane with area A if the plane were oriented in the xz plane at y = y0?

What would be the electric flux if the plane were oriented in the yz plane at x = x0?

Quiz

Suppose there was an electric field given by

€

rE = α y

r i x

What would be the electric flux through a front side of a cube of side L?

Quiz

Electric flux through a sphere

A positive point charge q=3.0 C is surrounded by a sphere with radius 0.2 m centered on the charge. Find the electric flux through the sphere due to this charge.

Definition of a solid angle

S

;2R

S

does not depend on radius

The largest 24 RS

Then

2R

dSd

4

42

2

R

R

S

enclosedQSdE

0

Chasing the tail: Electric field of a single fixed charge

204

1

r

QE

Have a great day!

Please don’t forget your pictures

Hw: All Chapter 4 problems and exercisesReading: Chapter 5