To simplify the situation, we will usually make some sort of assumption. For example, //__we often assume that the charge(s) are fixed in place__// (something is holding them at a particular location, but we don't care what that something is). Or //__we will assume that we are interested in a particular instant in time__// and examine what is happening for that situation (like taking a single frame from a movie or freezing time).
To simplify the situation, we will usually make some sort of assumption. For example, //__we often assume that the charge(s) are fixed in place__// (something is holding them at a particular location, but we don't care what that something is). Or //__we will assume that we are interested in a particular instant in time__// and examine what is happening for that situation (like taking a single frame from a movie or freezing time).
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=== How useful is this assumption? ===
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==== How useful is this assumption? ====
[{{ 184_notes:dipole.png?150|Dipole representation - one positive and one negative charge, separated by a distance d}}]
[{{ 184_notes:dipole.png?150|Dipole representation - one positive and one negative charge, separated by a distance d}}]
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[{{ 184_notes:dipole_epoint.png?150|Electric field at a single point (Point P) due to a dipole}}]
[{{ 184_notes:dipole_epoint.png?150|Electric field at a single point (Point P) due to a dipole}}]
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[[184_notes:pc_efield|As you have learned]], the electric field from a single //positive charge// at any given point will point away from the charge, and the electric field at any given point from a //negative charge// will point toward the point charge. So what happens to the electric field when you have a positive charge next to a negative charge? The field at any point in space around the two charges will be given by a **net electric field**, which is the [[184_notes:math_review#vector_addition|vector addition]] of the electric field from the positive charge and the electric field from the negative charge.
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[[184_notes:pc_efield|As you have learned]], the electric field from a single //positive charge// at any given point will point //away// from the charge, and the electric field at any given point from a //negative charge// will point //toward// the point charge. So what happens to the electric field when you have a positive charge next to a negative charge? The field at any point in space around the two charges will be given by a **net electric field**, which is the [[184_notes:math_review#vector_addition|vector addition]] of the electric field from the positive charge and the electric field from the negative charge.
→Enet=→E++→E−
→Enet=→E++→E−
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==== Superposition of Electric Potential ====
==== Superposition of Electric Potential ====
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[{{ 184_notes:potentialgraph.jpg?300|Potential vs Distance graph of a positive (blue) and a negative (red) charge with the V=0 reference point at r=∞.}}]
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[{{ :184_notes:electricpotential_new_2.png?300|Potential vs Distance graph of a positive (dashed blue) and a negative (solid red) charge with the V=0 reference point at r=∞.}}]
Because electric potential is a scalar, it means adding together the electric potentials can be quite a bit simpler than adding electric fields (you don't have to consider direction); however, you must first check that the reference point for each of the individual potentials is the same. This is the same idea that we used with [[183_notes:relative_motion|relative motion]] when we had to choose where the origin was to make measurements of displacements - it doesn't make sense to compare measurements with two different origins. The **reference point** for potential is typically defined as the location where the electric potential is equal to zero. You can find the reference point by setting V = 0 and solving for the position, r, or by graphing the electric potential versus distance and finding the location where V=0. **//You can only add potentials that have the same reference point//**.
Because electric potential is a scalar, it means adding together the electric potentials can be quite a bit simpler than adding electric fields (you don't have to consider direction); however, you must first check that the reference point for each of the individual potentials is the same. This is the same idea that we used with [[183_notes:relative_motion|relative motion]] when we had to choose where the origin was to make measurements of displacements - it doesn't make sense to compare measurements with two different origins. The **reference point** for potential is typically defined as the location where the electric potential is equal to zero. You can find the reference point by setting V = 0 and solving for the position, r, or by graphing the electric potential versus distance and finding the location where V=0. **//You can only add potentials that have the same reference point//**.
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Most of the time, //__we assume V=0 is at infinity__//. We actually already made this assumption when we said the [[184_notes:pc_potential|electric potential for a point charge]] is V=14πϵ0qr (the only time when V=0 is when r=∞). The potential vs distance graph for a positive charge (in blue) and a negative charge (in red) is shown in the figure to right.
Most of the time, //__we assume V=0 is at infinity__//. We actually already made this assumption when we said the [[184_notes:pc_potential|electric potential for a point charge]] is V=14πϵ0qr (the only time when V=0 is when r=∞). The potential vs distance graph for a positive charge (in blue) and a negative charge (in red) is shown in the figure to right.
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[{{ 184_notes:potentialgraphshift.jpg?300|Potential vs Distance of a positive (blue) and a negative (red) charge with the V=0 reference point at a non-infinite reference point.}}]
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[{{ :184_notes:electric_potential_non_infinite_reference_new.png?300|Potential vs Distance of a positive (dashed blue) and a negative (solid red) charge with the V=0 reference point at a non-infinite reference point.}}]
However, we could have equally said the voltage for a point charge was V=14πϵ0qr−2, which would give us a reference point at rrp=14πϵ0q2. The electric potential vs distance graphs for this potential/reference point are shown to the right (again, with blue for a positive charge and red for a negative charge). There is nothing wrong with having a different reference point, but we will usually pick a reference point at r=∞ because it makes interpreting voltage numbers easy: a (+) voltage means you are close to a positive charge, a (-) voltage means you are close to a negative charge, and a zero voltage means you are either at r=∞ or somewhere in between a positive and negative charge. //Sometimes it's convenient to set the potential to zero at somewhere other than r=∞, which we will do when we discuss circuits.//
However, we could have equally said the voltage for a point charge was V=14πϵ0qr−2, which would give us a reference point at rrp=14πϵ0q2. The electric potential vs distance graphs for this potential/reference point are shown to the right (again, with blue for a positive charge and red for a negative charge). There is nothing wrong with having a different reference point, but we will usually pick a reference point at r=∞ because it makes interpreting voltage numbers easy: a (+) voltage means you are close to a positive charge, a (-) voltage means you are close to a negative charge, and a zero voltage means you are either at r=∞ or somewhere in between a positive and negative charge. //Sometimes it's convenient to set the potential to zero at somewhere other than r=∞, which we will do when we discuss circuits.//
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==== Examples ====
==== Examples ====
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[[184_notes:examples:Week3_superposition_three_points|Superposition with Three Point Charges]]
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* [[184_notes:examples:Week3_superposition_three_points|Superposition with Three Point Charges]]
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* Video Example: Superposition with Three Point Charges
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[[184_notes:examples:Week3_plotting_potential|Plotting Potential for Multiple Charges]]
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* [[184_notes:examples:Week3_plotting_potential|Plotting Potential for Multiple Charges]]