Ch3 Quiz 1

First name______________________ Last name ___________________

Section number______

There is an electric field given by

xiEE

0

where E0 is a constant. What is the difference in the value of the electric potential due to this electric field between the origin and the point x=a, y=b?

Ch3 Quiz 3

There is an electric field created by some source at the origin given by

rir

cE

4

where c is a constant and r is the distance from the origin; points out from the origin. What is the difference in the value of the electric potential due to this electric field between the point x=a, y=b and the point at infinity?

ri

What is the potential function corresponding to this electric field if instead of being at the origin the source of the electric field is at point x=a, y=b?

Ch3 Quiz 2

First name______________________ Last name ___________________

Section number______

There is an electric field given by

yx iyixE

22

where and are constants. What is the difference in the value of the electric potential due to this electric field between the origin and the point x=a, y=b?

In electrostatics:

y

UF

x

UF yx

y

VE

x

VE yx

If we know V(x,y) we can find the components of electric field and xE yE

In electrostatics, the electric field is conservative:

0rdE

1)The electric potential V in a region of space is given by

)3(),( 22 yxAyxV where A is a constant. Derive an expression for the electric field at any point in this region.

2)The electric potential V in a region of space is given by

33)(

r

crV

where c is a constant. The source of the field is at the origin. Derive an expression for the electric field at any point in this region.

Exercise 5 p. 52

An electron moves from one point to another where the second point has a larger value of the electric potential by 5 volts. If the initial velocity was zero, how fast will the electron be going at the second point?

Electric potential V is a scalar!

An old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hourAn old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hour

Electric field lines

These are fictitious lines we sketch which point in the direction of the electric field.

1) The direction of at any point is tangent to the line of force at that point.

2) The density of lines of force in any region is proportional to the magnitude of in that regionE

E

Lines never cross.

1R2R

Density is the number of lines going through an area (N)

divided by the size of the area

21

14 R

NdensityRAt

22

24 R

NdensityRAt

24 r

NdensityranyAt

204

1

r

qE

For a charge q located at the origin

Edensity

It is important that the force is proportional to 21

r

Gauss’s Law

The total flux of electric field out of any closed surface is equal to the charge contained inside the surface divided by .0

S

enclosedQSdE

0

What is or flux of any vector, e.g. velocity of a water flow?

SdE

Consider a flow with a velocity vector . Let S be a small area perpendicular to .

v

v

a) The volume of water flowing through S per unit time is vS

S

a)

v

b) Now S is tilted with respect to . The volume of water flowing through S per unit time is

vcosvS

n

S

b)

vnSS

Area vector

is the angle between velocity vector and unit vector

normal to the surface S.

v

n

SvvS

cosFlux:

S S

Flux of electric field E

Hw quiz

Suppose Coulomb’s Law for the force between charges and was

rr

qqF ˆ

421

with some constant. Find the potential function corresponding to such a force and the electric potential function.

1q2q

Have a great day!

Please don’t forget your pictures

Hw: All Chapter 3 problems and exercisesReading: Chapter 3