University Physics Volume 2

# Summary

### 7.1Electric Potential Energy

• The work done to move a charge from point A to B in an electric field is path independent, and the work around a closed path is zero. Therefore, the electric field and electric force are conservative.
• We can define an electric potential energy, which between point charges is $U(r)=kqQrU(r)=kqQr$, with the zero reference taken to be at infinity.
• The superposition principle holds for electric potential energy; the potential energy of a system of multiple charges is the sum of the potential energies of the individual pairs.

### 7.2Electric Potential and Potential Difference

• Electric potential is potential energy per unit charge.
• The potential difference between points A and B, $VB−VA,VB−VA,$ that is, the change in potential of a charge q moved from A to B, is equal to the change in potential energy divided by the charge.
• Potential difference is commonly called voltage, represented by the symbol $ΔVΔV$:
$ΔV=ΔUqorΔU=qΔV.ΔV=ΔUqorΔU=qΔV.$
• An electron-volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
$1eV=(1.60×10−19C)(1V)=(1.60×10−19C)(1J/C)=1.60×10−19J.1eV=(1.60×10−19C)(1V)=(1.60×10−19C)(1J/C)=1.60×10−19J.$

### 7.3Calculations of Electric Potential

• Electric potential is a scalar whereas electric field is a vector.
• Addition of voltages as numbers gives the voltage due to a combination of point charges, allowing us to use the principle of superposition: $VP=k∑1NqiriVP=k∑1Nqiri$.
• An electric dipole consists of two equal and opposite charges a fixed distance apart, with a dipole moment $p→=qd→p→=qd→$.
• Continuous charge distributions may be calculated with $VP=k∫dqrVP=k∫dqr$.

### 7.4Determining Field from Potential

• Just as we may integrate over the electric field to calculate the potential, we may take the derivative of the potential to calculate the electric field.
• This may be done for individual components of the electric field, or we may calculate the entire electric field vector with the gradient operator.

### 7.5Equipotential Surfaces and Conductors

• An equipotential surface is the collection of points in space that are all at the same potential. Equipotential lines are the two-dimensional representation of equipotential surfaces.
• Equipotential surfaces are always perpendicular to electric field lines.
• Conductors in static equilibrium are equipotential surfaces.
• Topographic maps may be thought of as showing gravitational equipotential lines.

### 7.6Applications of Electrostatics

• Electrostatics is the study of electric fields in static equilibrium.
• In addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink jet printers, and electrostatic air filters.