Equipotential and Electric Field Lines

Electric Field (E)

For a point charge:
\[ E = \frac {kₑ . q }{ r^2}\] Where:
\[kₑ = 8.988×10^9 \]N·m²/C² (Coulomb's constant)
q = charge magnitude
r = distance from the charge

Electric Potential (V)

For a point charge:
\[V =\frac{ kₑ . q}{ r}\] For two charges:
\[ V_{total}= kₑ(\frac {q_1}{r_1} + \frac {q_2}{r_2} )\]

Equipotential Lines

Imaginary surfaces where the electric potential is equal at all points.
Their properties:

• They are perpendicular to electric field lines
• They do not intersect with each other
• For single charges, they are spherical in shape

Electric Field Lines

Imaginary lines showing the direction and strength of the electric field:
←←← (for negative charge)
→→→ (for positive charge)

• Start from positive charge and end at negative charge
• Their density is proportional to field strength
• Do not intersect

Comparison Between Them

Equipotential and Electric Field
 
Question: Can a charge move between two points in an electric field without doing work?
When we move a charge between two points that have the same potential, we do no work on the charge because it has the same potential
For a single point charge, points that have the same distance from the charge have the same potential
For two point charges of different types, equipotential points resemble those of single charges
But the field differs in the region between the two charges Two point charges of different types
Equipotential points exist around each charge, the shape of equipotential points and the field differs in the region between the two charges
In this simulation, you can adjust the charge and position of the two charges using sliders or input boxes. The sliders work
but they don't work smoothly due to the complexity of calculations
So it might be better for you to use input boxes
Choose the 3D view and the electric potential appears as a third dimension
Choose the equipotential view and you'll see a 2D view with equipotential lines displayed
In this view, you can also choose to see vectors showing the direction of the electric field