Electric Potential

Electric Potential

Coulomb’s Law Q1 rQ2 If either Q1 or Q2increases the Force increases If either Q1 or Q2decreases the Force decreases If r, the distance between the two charges, increases the force decreases If r, the distance between the two charges, decreases the force increases Because r appears as 1/r2 the dependence on r is strong

Coulomb’s Law Q1 rQ2 Double r. F decreases by a factor of 4 If r -> r/3 F increases by a factor of 9 If r decreases to ¼ of its value, F becomes 16 times as large

The Electric Field The electric field is the force on a small charge, divided by the charge:

Fields play an intermediate role in the force between bodies. We treat fields as a property of space. Charges create fields. Given the field we can calculate the forces on ANY charged objects

Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant.

Potential Energy The presence of charges can give rise to a potential energy (PE)

Potential Energy We determined the potential energy Uel of a spring by asking how much work we do to compress it. We can determine the potential energy of a charge distribution by how much work we do to bring the charge to its position

Potential of a Parallel-Plate Capacitor Slide 21-24

Potential Energy • High Gravitational PE. Ball will roll down hill • High Electrical Potential Energy • Positive charge will move away • Positive charge will “fall” from high • potential energy to low PE + • Negative charge “falls” from high PE to • low PE -

Electrostatic Potential Energy Change in electric potential energy is work done against electric force: PEa – PEb = qEd a--- Compare Ug b--- Ug = mg (a-b) =mgh

Electric Potential • Just as Electric field depends on space and allows us to compute force on any charge Electric Potential depends on space and allows us to calculate Uelec for any charge.

Electrostatic Potential Energy and Potential Difference Electric potential is defined as potential energy per unit charge: Unit of electric potential: the volt (V). 1 V = I J/C.

Ue= qV

Ue= q V Ue(B) = 10 nC * 400V

Electrostatic Potential Energy and Potential Difference Analogy between gravitational and electrical potential energy:

A A and B are the same distance from sphere B Which has higher potential energy A, B or C the same?

A A and B are the same distance from sphere B Which is at a higher potential A,B or C the same?

Electrostatic Potential Energy and Potential Difference Only changes in potential can be measured, allowing free assignment of V = 0. Vba = Vb – Va = Ue(b) –Ue (a) q

Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector.

Is the change in UeΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f? + if

Is the change in UeΔU, A) positive B) negativeC) zeroas a negative charge moves from point labeled i to f? + if

Is the change in UeΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f? +- i f

Conceptual Example Problem • The correct order of electrical potentials • from largest to smallest is • V1>V2>V3 • V1=V2> V3 • V1=V2 =V3 • V3>V2=V1 • V3>V2>V1 Slide 21-17

Energy Conservation in Electric Potentials • Just as for mechanical systems Energy is conserved. We can change potential energy to kinetic energy and vice versa. • Kf + qVf= Ki + qVi • Kf –Ki= qVi –q Vf =-q(Vf –Vi) ΔK = -qΔV

Charged Particle Moving Through a Potential Difference ΔK = -qΔV Slide 21-18

Charged Particle Moving Through a Potential Difference Be careful! Things are reversed for negative charge. Negative charge speeds up if it moves from region of lower to higher potential: ΔK = -qΔV Slide 21-18

The Electron Volt, a Unit of Energy One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt.

Slide 21-19

Example Problem A proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point? Slide 21-20

Electric Potential