In what ways is the acceleration due to gravity similar/different from the electric field?

Answer 1

The acceleration due to gravity comes from the Newton's universal law of gravitation.

F = G * m_1 * m_2 /(r^2) , which is the force of attraction between two massive bodies, of masses m_1 and m_2 separated by a distance r along a straight line joining them.

Now if one of the massive bodies is the earth (or a planet or the moon) then the force of attraction divided by the mass of the second body is an acceleration, called the acceleration due to gravity. Note that, according to Newton's second law of motion, force acting on a body will produce an acceleration (or change of velocity) :

a = F/m ( acceleration = force/mass)

Hence, from Newton's second law:

g = F_gravitation / m_2
= G * m_1 /r^2
= G * M_{earth} /R^2
= acceleration due to gravity

where, R is the radius of the earth or a planet, when the second body is on the surface of the earth. If the second body is above a height h from the surface, since we can neglect the mass of air from the surface to the height h, compared to the mass of the earth,

g = G * M_{earth} /(R+h)^2


Now we answer your question:
Similarities:
1. Both the electric field and the acceleration due to gravity obey inverse square law.

2. Both are vector fields, i.e. at each point in space, there is a magnitude of the physical quantity and a direction associated with it.

3. Both are force per unit charge of the monopole of the field. Here mass is the monopole of gravitation and electric charge is the monopole of electric force.

Dissimilarities:
1.Acceleration due to gravity is always directed towards to the centre of mass a massive body (i.e. the centre of a spherical object). But electric field can be both directed towards and directed away from a electric charge, depending on the polarity of the charge.

Cheers.

Answer 2

Similar in that it obeys an inverse square law. Different in that there are no 'repulsive' gravitational fields.


Doug