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Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
Isolines, also known as contour lines, are lines that connect points of equal value in a scalar field. In the context of electric fields, isolines are used to represent points of equal electric potential.
Here are some key points about isolines as related to electric fields:
Electric potential and voltage are related concepts that describe the potential energy of a charged particle in an electric field.
Here are some key points about electric potential and voltage:
The equation for electric potential is derived based on the equation from electrical energy which we will learn about next! For now just take our word.
The left-hand side of this equation shows the work (or amount of energy) per unit of charge. This "work per charge" quantity is called electric potential or voltage (V).
** W or UE is electric potential energy, measured in Joules. It is NOT the same as potential difference, V, measured in Joules/Coulomb.**
** Like energy, voltage is a SCALAR. The change may be positive or negative, but that doesn't imply directionality!**
Electric Potential of a Point Charge
Let's say you had a positive charge and wanted to map the potential difference around it. The electric field lines move AWAY from the charge. Since V=kQ/r, we can find equal voltages at equal radii from the charge. The equipotential lines would, therefore, look like concentric circles around the charge. Notice how each field line (blue arrows) intersects at 90 degrees with the equipotential lines
Image from openstax.org
Since the electric field strength decreases as the radius increases, the voltage must also be decreasing as we travel further away from the charge.
Equipotential lines are lines in an electric field that represent points of equal electric potential.
Here are some key points about equipotential lines:
Other connections: The idea of equipotential lines with voltage is very similar to topographical maps or barometric pressure maps you may have created in an Earth Science class. In each case, the lines drawn represent areas with the same value: height for topographical maps and pressure for barometric pressure maps.
In rare cases you could be asked to draw an arrow representing the electric field on a map of electric potentials. In that case draw an arrow perpendicular to the curve pointing from high potential to low potential.
Practice Question:
a) Describe the direction of the electric field at point A
b) At which point is the electric field have the greatest magnitude?
c) How much net work must be done by an external force to move a -1mu C point charge from rest at point C to rest at point E? (Can be answered after learning the next objective)
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