Electricity and Gravity

Yeah, yeah, don’t even think about telling me these two things are related!

How Are Electricity and Gravity Related???

• Both transmit their effects over a distance

• Both directly depend upon properties of the objects undergoing the interaction (mass for gravity and charge for electricity)

• Both drop off as 1/(separation)2

Just as There’s a Gravitational Field, There’s an Electrical Field

The Earth (and all masses) possess gravitational fields; all charges, such as protons, possess electrical fields.

p

Mass (for Gravity) and Charge (for Electricity) are Analogous

We can easily visualize mass; it’s an everyday phenomenon; unlike electric charges, though, there are no known negative masses.

m q

Charge is harder to visualize as there are usually both positive and negative charges within an object, which can cancel each other out.

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Mass, measured in kilgrams (kg) Charge, measured in Coulombs (C)

The Force Equations for Gravity and Electricity are Very Similar

m1

m2

separation = s

Fgravity = Gm1m2

s2

separation = s

q1

q2

Felectricity = kq1q2

s2

How Similar Are Those Equations?

• Both require two objects to be influencing each other

• Both depend upon the separation of those objects in exactly the same way, 1/s2

• Both depend upon properties of each object (masses for gravity, charges for electricity)

• Both have a multiplicative constant (G = 6.67x10-11 N·m2/kg2 for gravity

k = 8.99x109 N·m2/C2)

Electric Fields and Electric Potential (aka, “Voltage”)

For a positive charge, field lines radiate outwards

For a negative charge, field lines point inwards

Topographic Maps

A topographic map, like this of Mt. Fuji in Japan, shows curves which are all at equal altitude.

Imagine a mountain that, seen from any side, looks like the figure below:

Ground Level

From overhead, the topographic map of this mountain would be of concentric circles:

Placing a rock at various points on the mountain and watching what possible paths the rock takes as it rolls down would give the following:

Similarly, if we have a fixed positive charge instead of a mountain and we place a moveable charge in the vicinity, the motion of the charge would look like the motion of the rock:

The red arrows shown are the electric field lines for the fixed positive charge!

If, instead of a mountain, we had an undersea valley, the trajectory of the rock would be towards the bottom of the valley:

In the context of electric charges, the undersea valley is analogous to negative charges, with the electric field lines shown pointing towards it:

Electric field lines point away from a positive charge and towards a negative charge.

Extending this analogy, if we had a mountain peak near an undersea valley, the possible trajectories of the rock would be:

This picture gets quite messy when we include the topographic lines of equal altitude, but here goes:

In the analogy, the topographic lines represent curves at equal VOLTAGE (aka Electric Potential)

Notice that the electric field lines are always perpendicular to the curves of equal voltage.

Notice also that you can be at a positive potential, zero potential, or negative potential.

With our analogy, we can “derive” an expression for electrical potential energy similar to that of gravitational potential energy:

GPE = m g h EPE = q E x

Property of Object Within Field

Strength of Field

Relative Location of Object Within Field

Regrettably, the analogy in gravity for the concept of voltage in electricity is not convenient; the math gets phenomenally ugly because we often have to treat more complicated situations in gravity. Fortunately, making the analogy between voltage in electricity and height in gravity isn’t completely spurious.

GPE = mgh = m EPE = qEx = qV

The analogous concept in gravity would be to combine g and h into one, all-encompassing term, but it gets rather more complicated than that.

What Should You Take From This?

• The electrical force between two charges is similar to the gravitational force between two masses

• Charge is the electrical equivalent of mass

• Electric field lines exist when charges are present

• Electric field lines represent the possible trajectories a moving positive charge could take

• Voltage in electricity is reasonably analogous to height in gravity