~ Electric Charge & Force ~

E & M: a Saint Ann's Study of I & P

Daniel A. Martens Yaverbaum

Due November 18, 2014

I. point charges.

    The charges and coordinates of two charged particles held fixed in an xy plane are q₁ = +3.0 microC, x₁ = 3.5 cm, y₁ = .50 cm and q₂ = -4.0 microC, x₂ = -2.0 cm, y₂ = 1.5 cm.

a) Draw a neat and clear diagram of the situation.

Find the

b) magnitude and

c) direction of the electrostatic force exerted on particle 2 by particle 1. 

Find the

d) magnitude and

e) direction of the electrostatic force exerted on particle 1 by particle 2.

f) At what coordinates (x and y) should a third particle of charge q3 = +4.0 microC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?

g) Assume that particle 3 sits at the coordinates you found in part (f), above.  What is the net electrostatic force on particle 3 due to particles 1 and 2?

II. symmetry.

    A large, solid, insulating sphere has charge +Q distributed uniformly throughout its volume.  The 3-D charge density, q/V, is a constant  You can call this constant ρ if you like. The radius of the charged sphere is R.

    A small test charge, -q is placed somewhere in the body at an arbitrary displacement from the center, r.

 a) Derive and/or justify an expression that describes how the electrostatic force exerted on -q by +Q varies as a function of r.

 b) Assume that +Q = +15 microC and R = 30 cm (very large ball of very large charge!).

        ALSO NOTE: The mass of one electron is always given by m_e= 9.11 x 10^-31 kg and the charge magnitude of one electron is e = 1.60 x 10^-19 C.

                                    You can therefore get a constant value for the mass/charge ratio.

    If that small test charge, -q, is placed somewhere on the surface of the sphere and then allowed to fall all the way through an evacuated diameter:

    How much time will it take for the test charge to reach the opposite surface of the sphere?

    (Deja vu?)

  c) If the test charge had been +q, rather than -q, how would your responses to (a) and (b) change? (Answer in words, not in numbers.)

 d) If the sphere of charge +Q had been made of conducting material, rather than insulating material, how would your responses to (a) and (b) change? (Answer in words, not in numbers.)

III. scale.

A cup of water, 250 ml, is placed 10 meters away from another cup of water, same size.

The density of water is approximately 1 g/ml and there are approximately 18 grams of water per 1 mole (6 x 10²³) of molecules.

The charge magnitude of a proton is the same as that of an electron: 1.60 x 10^-19 Coulombs.  The mass of an electron is approximately 9.11 x 10^-31 kg.

                a) In Newtons, how strong is the force of  electrostatic attraction that the protons in one cup exert on the electrons in the other cup?

    b) In Newtons, how strong is the force of electrostatic repulsion that the electrons in one cup exert on the electrons in the other cup? (If you get involved in too many computations for this one, something has gone wrong.)

                c) In Newtons, how strong is the force of GRAVITATIONAL attraction that the electrons in one cup exert on the electrons in the other cup?

                d) By how many orders of magnitude do the gravitational and electrostatic forces differ--all other things being equal?