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 4 He nucleus Because the 4 He nucleus has four nucleons, two of which are protons, Z decreases by 2 and A decreases by 4 The 4 He 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. The number of protons changes, so the element changes. Though energy, momentum, angular momentum, nucleon number, and charge is conserved. 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. Another mechanism for light nuclei decay.

Gamma Decay The nucleus can lose the energy by emitting a gamma ray (high energy photon) After a nucleus undergoes a radioactive decay, the nucleus is often in an excited state.

Quiz T Two 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 B A)Greater B)Smaller C)The same.

Coulomb’s Law Like charges repel, unlike charges attract Force is directly along a line joining the two charges q1q1 q2q2 r An inverse square law, just like gravity Can be attractive or repulsive – unlike gravity Constant is enormous compared to gravity  0 =  C 2 / (N●m 2 ) 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

Electric Field Lines Consider 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 A region of space has an electric field of 10 4 N/C, pointing in the plus x direction. At t = 0, an object of mass 1 g carrying a charge of 1  C is placed at rest at x = 0. Where is the object at t = 4 sec? A) x = 0.2 mC) x = 20 m B) x = 0.8 mD) x = 80 m

Quizzes 2 A cube with 1.40 m edges is oriented as shown in the figure Suppose there is a charge situated in the middle of the 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/6  o B)q/4  o 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 = E n A= EA cos  EnEn For a non-constant electric field, or a curvy surface, you have to integrate over the surface 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? Answer is always 4  k e q charge q

Quiz –An electron is accelerated from rest through a potential difference V. Its final speed is proportional to: –A) V 2 –B) V –C) V 1/2 –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 / d 2 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 Electric Fields are doing work on the charge If path is not a straight line, or electric field varies you can rewrite this as an integral

Electric Potential Electric Field E Point A Point B Path you choose does not matter. (conservative) Factor out the charge – then you have electric potential V

Each of the Capacitors above has a capacitance of 12 pF. What is the combined capacitance of the whole system? A)12 pFC) 8 pF B)4 pFD) 20 pF

Combining Capacitors: Series wire (conductor) capacitor switch battery +– Charges are the same on each capacitor Voltages add In Series: C1C1 C2C2 C3C3

Combining Capacitors: Parallel wire (conductor) capacitor switch battery +– C1C1 C2C2 C3C3 In Parallel: Same Voltages Voltages are the same across each capacitor Charges add

Capacitors and Dielectrics d area A Dielectric constant  A dielectric changes the capacitance Cause a breakdown potential, V max 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 This is equivalent to saying that the resistivity of the material is independent of the applied field

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  V 1  +  V 2 +  V 3 = 0 I3I3 I2I2 I1I1 I 3 =I 2 +I 1

+–+–  9 V 5   9 V Odd Circuit What is the current through the resistor? A) 3.6 A B) 1.8A C) 90 A D) 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 to ½ its final charge? Which circuit takes the least amount of time to charge the capacitor to ½ its final charge?

RC circuits Capacitor/resistor systems charge or discharge over time Charging:  is the time constant, and equals RC. Discharging: 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 S1S1 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: Close S 1 The result is a differential equation.