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Practice Problem I 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

Practice Problem II A cube with 1.40 m edges is oriented as shown in the figure Suppose the cube sits in a uniform electric field of 10i ? What is the magnitude of the flux through the whole cube? What is the magnitude of the flux through the top side? How many sides have nonzero flux? A)q/  o D) q/6  o B)q/4  o C)0 A)2D) 1 B)4 C)0

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

Quiz Points R and T are each a distance d from each of two equal and opposite charges as shown. Thework required to move a negative charge q from R to T is: A) kQq / (2d) B) kqQ / d C) kqQ / d 2 D) zero

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

Electric Potential – The zero point Like potential energy, the zero point of electric potential is arbitrary Two different conventions are used 1.When you are infinitely far away from all charges, the potential is zero (preferred by physicists) V = 0 2.The Earth is at zero potential (preferred by electrical engineers) V = 0

Electric Potential and Conductors No electric field, so no difference in electric potential Conductors have constant electric potential; whatever the value is at the surface Earth is a reasonable conductor Entire Earth is at same potential Any conductor connected to the Earth is grounded

Potential difference in constant field Electric Field Equipotential surfaces High Potential Low Potential Electric Fields are perpendicular to equipotential surfaces Positively charged particles are attracted to low potential areas (and vice versa) + -

What is the electric potential difference between the two plates? A)10 VD) 10 4 V B)10 2 V C)10 3 V Potential Difference between parallel plates 10 m 1 cm 1000 N/C Two plates 10 m on a side separated by 1 cm 1000 N/C electric field between them

Electric Potential from a point charge Equipotential surfaces and electric fields are perpendicular

Multiple charges q1q1 q2q2 q3q3 r1r1 r2r2 r3r3

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: T In a famous experiment, alpha particles (charge +2e, mass 6.64 x kg), were fired at a gold nucleus (charge +79e, assume it is stationary). In particular, suppose an alpha particle, initially very far from the gold nucleus, was fired directly towards the center of the nucleus with a velocity of 2.00 x 10 7 m/s. How close does the alpha particle get to the gold nucleus? A)~27fm B)~14fm C)~14  m D)~170Km Hint: Conservation of energy