Why is more fuel required for a spacecraft to travel fromthe Earth to the Moon than it does to return from the Moonto the Earth?

Physics 2080 Chapter 20: Electric Potential and Electric Potential Energy February 9, 2016 Amanda Biddlecome 1) Electric Potential Energy and the Electric Potential -‐electric force=conservative *has potential energy -‐takes work to move charge perpendicular to the field W=-‐q Ed 0 *W=work *q =ch0rge *E=electric field *d=distance ΔU=-‐W *ΔU=change in potential energy *W=work ΔU=qΔV *ΔU=change in potential energy *q=charge *ΔV=change in electric potential -‐electric potential is not the same as potential energy -‐ΔV is the potential difference *unit=Volt (V)=J/C -‐ΔU is the potential energy *unit=J -‐electron volt (eV) is a unit of energy *eV is the amount of energy it takes to move 1 electron across a potential of 1V *1 eV=(1.60X10 C)(1V)=1.60X10 J ‐19 -‐19 -‐potential difference is the change in potential energy of a charge that is moved from point A to point B which lie in a charge -‐positive charges gain electric potential energy when moved opposite to the electric field -‐negative charges lose electric potential energy when moved opposite to the electric field -‐the net potential is the sum of potential energies V=k(q /r +q1/r )1 2 2 *V=net potential *k=8.99X10 Nm /C 2 2 *q 1 and q 2charges (C) *r 1 and 2 =distance between charges (m) *potential difference is the same thing as voltage *potential difference can be measured by a voltmeter -‐electric field is related to how fast potential is changing E=-‐ΔV/ΔS *E=electric field *V=electric potential *ΔS=distance along the electric field *positive plate has the highest electric potential *negative plate has no electric potential *units of electric field are N/C or V/m *equipotential line=when two charges have a ΔS=0, they are along an equipotential line -‐electric potential decreases as you move in the direction of the electric field ΔV=V -‐V f i ΔV=-‐Ed *for ΔV to be positive, your field should move to the left 2) Energy Conservation -‐mass moves from point A to B due to conservative forces E =i f K +A =K +UA B B (1/2)mv +U =(1/2Amv +U A B 2 B (1/2)mv =(1/2)mvB+q(V -‐V ) A2 A B *E=electric field *K=kinetic energy *U=potential energy *m=mass *v=velocity *q=charge *V=voltage -‐decrease in electric potential energy corresponds to an increase in kinetic energy -‐force on the negative charge is opposite to field direction *positive charges accelerate in the direction of decreasing electric potential *negative charges accelerate in the direction of increasing electric potential *for both, charge moves to region of lower potential energy 3) Electric Potential of Point Charges -‐the difference in potential energy between points A and B U -AU =(kq qB/r -‐(kq q)/r0 A 0 B -‐electric potential for point charges V=kq/r -‐electric potential energy for point charges U=q V=(kq q0/r 0 -‐ideal conductor=equipotential surface *more curved surfaces have larger electric fields -‐electric fields in the human body *not perfect conductor *potential differences *electrocardiograph=heart *electroencephalograph=brain -‐electric potential=scalar characteristic of electric field -‐regions of space at the same electric potential=equipotential surfaces *always perpendicular to electric field when they intersect 4) Capacitors=application -‐2 conducting plates separated by a distance *positive and negative plates of the same magnitude -‐conductors that can store energy -‐takes work to store charges on a conductor *so stores energy as well -‐maximum potential of the capacitor=maximum potential of a battery -‐capacitor=2 conductors separated by an insulator -‐for energy to flow through a battery, have to have a completely closed loop -‐characterized by capacitance *depends on the geometry of the capacitor *units=Farads=C/V C=Q/ΔV or Q=CΔV *C=capacitance *Q=charge *V=potential difference *capacitance is always positive -‐capacitance: proportional to cross sectional area and inversely proportional to the distance between the plates *the bigger and closer the plates, the greater the capacitance *parallel plate capacitors are separated by air C=ε (A/d0 *C=capacitance -‐12 *ε =0missivity of space=8.85X10 *A=cross sectional area *d=distance -‐discharge of capacitance produces sparks *work is required to do this W=(1/2)QΔV Q=CV W=(1/2)CVΔV W=(1/2)CV 2 V=Q/C W=(1/2)Q(Q/C) 2 W=(1/2)Q /C *all of these are equivalent to one another and can be used interchangeably *W=work *Q=charge *V=potential difference *C=capacitance -‐dielectric=insulating material *fills the space of the air gap in a plate capacitor so it can’t be damaged *has constant (k) that depends on the material of the insulator C=kε (A/d)0 -‐can look at the total energy stored U=QV =(1/2)AV=(1/2)CV =Q /2C 2 2 *all equivalent -‐electric energy density U =Electric energy density=electric energy/volume=(1/2)ε E 0 2