Lecture 6 Chapter 25 The Electric Potential Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii
Today we are going to discuss: Chapter 25: Section 25.4-7 Electric Potential
Quantities describing: Interactions between charges The electric potential Consider a charge Q which creates an electric field Vectors Q Scalars (Force - vector) If F is conservative q V (potential energy - scalar) U Field Similar to the way we introduced the electric field instead of a force (to remove q), we can introduce the ELECTRIC POTENTIAL instead of the potential energy The unit (Electric field) (Electric potential)
Once the potential has been determined, it s easy to find the potential energy V(r) It is similar to
The Electric Potential Inside a Parallel-Plate Capacitor E V Es q The potential energy of q in a uniform electric field U qes The electric potential (definition) So V Es where s is the distance from the negative electrode The electric potential inside a parallel-plate capacitor s 0 s d s V C The potential difference V C, or voltage between the two capacitor plates is V V Ed 0 Ed
Equipotential surfaces V Es E s 0 Equipotential surfaces s d An equipotential surface/line is one on which all points are at the same potential The electric field vectors are perpendicular to the equipotential surfaces s
The Electric Potential of a Point Charge Q r q We derived the potential energy of the two point charges 1 4 The electric potential due to a point charge Q is 1 4 It s a scalar This expression for V assumes that we have chosen V = 0 to be at r =. Equipotential lines The potential extends through all of space, showing the influence of charge Q, but it weakens with distance as 1/r.
ConcepTest Which two points have the same potential? Equipotential of Point Charge A) A and C B) B and E C) B and D D) C and E E) no pair Since the potential of a point charge is: V k Q r only points that are at the same distance from charge Q are at the same potential. This is true for points C and E. B E Q C D A They lie on an equipotential surface. Follow-up: Which point has the smallest potential?
Equipotential surfaces
The principle of superposition If there are many charges. The electric potential, like the electric field, obeys the principle of superposition. Q 1 r 1 P -Q 2 r r 2 r3 1 1 1 4 4 4 Q 3 You see. The principle of superposition is so much easier with scalars
ConcepTest At the midpoint between these two equal but opposite charges, Equipotential of Point Charge A) E 0; V = 0 B) E 0; V > 0 C) E 0; V < 0 D) E points right; V = 0 E) E points left; V = 0 The principle of superposition + 0
ConcepTest Electric Potential What is the electric potential at point A? 1 4 A) V > 0 B) V = 0 C) V < 0 + 0 A B Since Q 2 (which is positive) is closer to point A than Q 1 (which is negative) and since the total potential is equal to V 1 + V 2, the total potential is positive.
ConcepTest Equipotential Surfaces At which point does V = 0? A B E) all of them C +Q Q D All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel out everywhere along the mid-plane between the charges. Follow-up: What is the direction of the electric field at all 4 points?
ConcepTest Four point charges are arranged at the corners of a square. Find the electric field E and the potential V at the center of the square. Hollywood Square A) E = 0 V = 0 B) E = 0 V 0 C) E 0 V 0 D) E 0 V =0 E) E = V regardless of the value The potential is zero: the scalar contributions from the two positive charges cancel the two minus charges. -Q +Q However, the contributions from the electric field add up as vectors, and they do not cancel (so it is non-zero). Follow-up: What is the direction of the electric field at the center? -Q +Q
The electric potential of a continuous distribution of charge
Example
Potential of a charged rod Determine the potential V(x) for points along the x axis outside the charged rod of length 2l. The total charge is Q. Let V=0 at infinity
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