Alpha-Decay•Very heavy nuclei are “crowded” – nucleons want to leave

•Although it is possible for them to emit single nucleons, this is very rare•Although it is possible for them to emit large particles, it is easier for them to emit small well-bound particles

•Such a particle is a 4He nucleus

238 234 492 90 2U Th He

•Because the 4He nucleus has four nucleons, two of which are protons, Z decreases by 2 and A decreases by 4 •The 4He nucleus is also called an - particle•This process is called alpha decay

Beta Decay•A neutron inside a nucleus is spontaneously decays into a proton, an electron, and an antineutrino.

1 1 -0 1n p e

•The number of protons changes, so the element changes.

•Though energy, momentum, angular momentum, nucleon number, and charge is conserved.

veNC 147

146

•A dominate mechanism for light nuclei.

Beta: Electron Capture

•A proton inside a nucleus absorbs an electron, and becomes a neutron

•The number of protons changes, so the element changes.

•Though energy, momentum, angular momentum, nucleon number, and charge is conserved.

vLieBe 73

74

•Another mechanism for light nuclei decay.

Gamma Decay

•The nucleus can lose the energy by emitting a gamma ray (high energy photon)

CC

veCB

126

*126

*126

125

•After a nucleus undergoes a radioactive decay, the nucleus is often in an excited state.

Quiz

• TTwo test charges are brought separately into the vicinity of a charge +Q.First, test charge +q is brought to point A a distance r from charge +Q. Next, the +q charge is removed and a test charge +4q is brought to point B a distance 2r from charge +Q. Compared with the electric field of the charge at A, the electric field of the charge at B is:

+Q +q

A+Q +2q

BA) GreaterB) SmallerC) The same.

Coulomb’s Law•Like charges repel, unlike charges attract•Force is directly along a line joining the two charges

q1 q2

r

•An inverse square law, just like gravity•Can be attractive or repulsive – unlike gravity•Constant is enormous compared to gravity

1 22

ˆee

k q qF r

r

1 2

20

ˆ4e

q qF r

r

0 = 8.85410-12 C2/ (N●m2) •Permittivity of free space

Electric Fields

•Electric Field is the ability to extert a force at a distance on a charge•It is defined as force on a test charge divided by the charge•Denoted by the letter E•Units N/C

+ +

+++

– – –

Small test charge q

F

/E F q

Electric Field LinesConsider the four field patterns below:

Assuming that there are no charges in the region of space depicted, which field pattern(s) could represent electrostatic field(s)?

Electric Field Lines•Graphical Illustration of Electrical Fields•Lines start on positive charges and end on negative•Number of lines from/to a charge is proportional to that charge•Density of lines tells strength of field.

+ -

- +

Electric Fields and Forces/E F q

F qE

A region of space has an electric field of 104 N/C, pointing in the plus x direction. At t = 0, an object of mass 1 g carrying a charge of 1C is placed at rest at x = 0. Where is the object at t = 4 sec?

A) x = 0.2 m C) x = 20 mB) x = 0.8 m D) x = 80 m

F ma

/a qE m

Quizzes 2A cube with 1.40 m edges is oriented as shown in the figure

Suppose there is a charge situated in the middle ofthe cube.• What is the magnitude of the flux through the

whole cube?• What is the magnitude of the flux through any

one side?

A) q/o D) q/6o B) q/4o C) 0

Electric Flux•Electric Flux is the amount of electric field flowing through a surface•When electric field is at an angle, only the part perpendicular to the surface counts

•Multiply by cos

E

E = EnA= EA cos

En

•For a non-constant electric field, or a curvy surface, you have to integrate over the surface

cosE E dA E dA

•Usually you can pick your surface so that the integration doesn’t need to be done given a constant field.

R

Electric Flux•What is electric flux through surface surrounding a charge q?

24E R E

4E ek q

2E ek q 2 ek q4 ek q

4 ek q22

4 ek qR

R

Answer is always 4keq

charge q

Quiz

– An electron is accelerated from rest through a potential difference V. Its final speed is proportional to:

– A) V2

– B) V– C) V1/2

– D) 1/V

Quiz

• Points R and T are each a distance d from each of two equal and opposite charges as shown. required to move a negative charge q from R to T is:

• • A) kQq / (2d)• B) kqQ / d• C) kqQ / d2

• D) zero

Potential Energy of charges•Suppose we have an electric field•If we move a charge within this field, work is being done

Electric Field E

charge q

W F s

qE s

•Electric Fields are doing work on the charge

U W qE s q E s

•If path is not a straight line, or electric field varies you can rewrite this as an integral

U q E ds

Electric Potential

Electric Field E

Point A

Point B

B

A

U q E ds

•Path you choose does not matter.(conservative)

•Factor out the charge – then you have electric potential V

B

A

UV E ds

q

Each of the Capacitors above has a capacitance of 12 pF. What is the combined capacitance of the whole system?

A) 12 pF C) 8 pFB) 4 pF D) 20 pF

12 12 24C 12

12

12

12

1 1 1 3 1

12 24 24 8C

24812 8 20C

Combining Capacitors: Series

wire (conductor)

capacitor

switch

battery+–

Charges are the same on each capacitorVoltages add

In Series:C1 C2 C3

1 2 3

1 1 1 1

C C C C

Combining Capacitors: Parallel

wire (conductor)

capacitor

switch

battery+–

C1 C2 C3

In Parallel:1 2 3C C C C

Same Voltages

Voltages are the same across each capacitorCharges add

Capacitors and Dielectrics

d

area A

0 AC

d

Dielectric constant

•A dielectric changes the capacitance•Cause a breakdown potential, Vmax to exist.

•Beyond the breakdown potential the dielectric starts to conduct!

Ohm’s Law

•The resistance R is a constant irregardless of the applied potential

Area A

V IR

•This is equivalent to saying that the resistivity of the material is independent of the applied field

EJ

Kirchoff’s Rules•The total current flowing into a point must equal the total current flowing out of a point [conservation of charge]•The total voltage change around a loop must total zero

+–

V

1

V

2

V

3

V1 + V2 + V3 = 0

I3

I2

I1

I3=I2+I1

+–

+–

9 V 5

9 V

Odd Circuit

What is the current through the resistor?

A) 3.6 AB) 1.8AC) 90 AD) 0 A

Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open.The values of the emf , resistance R, and the capacitance C for each of the circuits are

circuit 1:   18 V, R = 3  , C = 1 µF

circuit 2:   18 V, R = 6  , C = 9 µF

circuit 3:   12 V, R = 1  , C = 7 µF

circuit 4:   10 V, R = 5  , C = 7 µF

Which circuit has the largest current right after the switch is closed?

Which circuit takes the longest time to charge the capacitor to½ its final charge?

Which circuit takes the least amount of time to charge the capacitor to½ its final charge?

RC circuits•Capacitor/resistor systems charge or discharge over time

Charging: /

max/

max 11)( tRCt eQeQtq

is the time constant, and equals RC.

Discharging:/)( tQetq

Qualitatively: RC controls how long it takes to charge/discharge completely. This depends on how much current can flow (R)and how much charge needs to be stored (C)[As an exercise, show that RC has units of secs]

RC circuits: Prior to Steady-State

+–

E

R

S1

C

•Recall: the voltage across a capacitor is: V=q/C

•When the capacitor is fully charged the voltage

is ( e.g. it acts like a broken wire)•Prior, the voltage is V, i.e. there is a voltage drop.

Apply the loop rule: 0c

qiR

Close S1

0c

qR

dt

dqThe result is a differentialequation.