Question

INVESTIGATION 1: ELECTRICAL AND GRAVITATIONAL FORCES Let's begin our discussion with the familiar expression for the Coulomb force exerted on charge 2 by charge 1, F1-2 f12 Unit vector q1 r2 ,-8.99 × 109 Ncme C2 92 where k, is a constant that equals 9.0 x 10 N m2/C2. The force F2-1 of charge 2 on charge 1 is equal in magnitude and opposite in direction to F1-2 Coulomb did his experimental investigations of this force in the eighteenth century by exploring the forces between two small charged spheres. You have already examined the Coulomb force law in Lab 1.
Sorry there are so many parts to the question--thank you in advance for your effort.

Answer 1

1-1. Ans. Similarity between both forces;

• both the forces are central forces. (acts along the line joining both the masses/charges)
• and, forces are inversely proportional to the square of distance between the center of particles.

1-2. Ans. Difference;

• Gravitational forces are always attractive while electrostatic force can be either attractive or repulsive Depending upon nature of charges.

1-3. Ans. If there were negative mass, then two negative mass would attract each other (as two positive masses do attract)

and, in that case a negative and a positive mass would repel each other.

Theoretically it does rear it’s head, though it quite probably doesn’t exist in nature.

In Anti de-Sitter space (a particular kind of abstract spacetime background with constant negative curvature, unlike Minkowski space (the latter being flat)), it’s consistent for fields to have negative mass. This is ok in this context since energy is still bounded from below; commonly we think that negative energy is a big no-no but it’s sign just depends on what you call “zero energy”. You can have negative energy so long as energy can’t be any smaller than some given value; in this way you ensure that you can’t just infinitely borrow energy, which could permit perpetual motion, for instance.

Tachyon’s, the infamous superluminal-speed particles that make an appearance in string theory (until they’re surgically removed) and sci-fi literature have negative mass squared. Naively this is a huge problem because superluminal travel potentially permits violations of causality; the fact that physical occurrences in different people’s reference frames should have a unique ordering. Actually (as far as I’m aware) you can contrive a quantum field theory of tachyons that despite superluminal propagation does not allow one to transmit information locally faster than light, hence there’s no problem with causality. Now there may be something else evidently pathological about Tachyons but I’m honestly not sure.