Electric potential and electric potential energy - Electrostatics

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Electric potential and electric potential energy

Lessons

Notes:
In this lesson, we will learn:
  • The meaning of electric potential and electric potential energy
  • How to understand electric potential energy problems by analogy to gravitation problems
Notes:

  • Electric potential energy (Ep) is the energy stored in a charge due to its location in an electric field. For example, moving two like charges close together stores potential energy, since the charges repel each other. Separating opposite charges also stores potential energy, since the charges attract each other. It is similar idea to gravitational potential energy.
  • It is useful to calculate changes in electric potential energy using the concept of electric potential difference (ΔV\Delta V). An electric potential (VV) is the electric potential energy of a charge q, divided by q. ΔV\Delta V is the difference in VV between two points.

Electric Potential Energy (Two Point Charges)

Ep=kQ1Q2r2E_p = k \frac{Q_1 Q_2}{r^2}
Ep:E_p: electric potential energy, in joules (J)
k=9.00×109Nm2/C2k = 9.00 \times 10^9 N\centerdot m^2 / C^2 (Coulomb's constant)
Q1,Q2:Q_1, Q_2: charge on each body, in coulombs (C)
r:r: distance between charges, in meters (m)

Electric Potential Energy (Charge in Constant Electric Field)

Ep=qEdE_p=qEd
EE: electric field, in newtons per coulomb (N/C)
qq: charge that experiences the EE, in coulombs (C)
dd: distance from location chosen as Ep=0E_p=0 J, meters (m)

Electric Potential

V=EpqV=\frac{E_p}{q}
VV: electric potential, in volts (V)
EpE_p: electric potential energy, in newtons (N)
qq: charge that experiences the potential, in coulombs (C)

Electric Potential Difference

ΔV=VfVi=Wonqq=ΔEqq\Delta V=V_f - V_i = \frac{W_{on\;q}}{q} = \frac{\Delta E_q}{q}
ΔV\Delta V: electric potential difference, in volts (V)
Vi,VfV_i,V_f: electric potential at initial and final points, in volts (V)
qq: charge that experiences the potential, in coulombs (C)
WonqW_{on\;q}: work to move qq from the initial point to the final point, in joules (J)
ΔEq\Delta E_q: change in potential energy of ???????? between the initial and final points, in joules (J)

Useful Constants

k=9.00×109Nm2/C2k = 9.00 \times 10^9 N\centerdot m^2 / C^2 (Coulomb's constant)
e=1.60×1019Ce = 1.60 \times 10^{-19} C (Elementary charge. qproton=e,qelectron=eq_{proton}=e, q_{electron}=-e)
mproton=1.67×1027m_{proton}=1.67 \times 10^{-27} kg
melectron=9.11×1031m_{electron}=9.11 \times 10^{-31} kg

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Electric potential and electric potential energy

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