Where Is the Electric Field and Potential Zero for Two Point Charges on an Axis?

[Shackleford]

We haven't even had lecture over these chapters because of stupid Ike.

26) Two point charges, 3.4 micro C and -2.0 micro C, are placed .05 m apart on the x axis. At what points along the x-axis is (a) electric field zero and (b) the potential zero? Let V = 0 at r = infinity.

(a) It would be the same as (b).

E = k (Q1/r1^2) + k (Q2/r2^2)

(b) Va = Va2 + Va1 = k (Q2/r2a) + k (Q1/r1a)

= 0 = k ((-2 micro C/x) + ((3.4 micro C/(x + .05))

3.4 micro C x = 2 micro C x + .10 micro C

1.4 micro C x = .10 micro C

x = .071429 m

(34) Three point charges are arranged at the corners of a square of side L. What is the potential at the fourth corner (point A), taking V = 0 at a great distance?

+Q L -2Q

L L

-3Q L A

V = k (Q/r)

Va = Va1 + Va2 + Va3 = k ((3Q/L) + (Q/root 2 L) - (2Q/L) = (root 2 Q)/L

(58) An alpha particle (Q = +2e, m = 6.647 x 10^-27) is emitted in a radioactive decay with kinetic energy 5.53 MeV. What is its speed?

v = 1.63 x 10^7 ms^-1

(74) Four point charges are located at the corners of a square that is .08 m on a side. The charges, going in rotation around the square, are Q, 2Q -3Q, and 2Q, where Q = 3.1 micro C. What is the total electric potential energy stored in the system, relative to U = 0 at infinite separation?

U = k ((-8Q^2)/L + (Q^2)/(root 2 L) = -7.88 J

Negative energy?

 

[Gear300]

For (26), (a) is not necessarily the same as (b) (although I haven't evaluated the answers); electric field is a vector and electric potential is a scalar (one takes into account direction). For (74) you simply sum up the potential energies of each charge in respect to another (without repetition of pairs)...if your answer is right and you are unsure of having negative energy, that simply means the system is bounded: if 2 charges attract each other, you'll notice that the electric potential energy at each point is negative (it becomes 0 as they separate to infinite separation); therefore, the 2 charges are bounded to each other. If 2 charges repel each other, their electric potential energy at each point is positive; the 2 charges are not bounded to each other.

 

[Shackleford]

For (26), (a) is not necessarily the same as (b) (although I haven't evaluated the answers); electric field is a vector and electric potential is a scalar (one takes into account direction). For (74) you simply sum up the potential energies of each charge in respect to another (without repetition of pairs)...if your answer is right and you are unsure of having negative energy, that simply means the system is bounded: if 2 charges attract each other, you'll notice that the electric potential energy at each point is negative (it becomes 0 as they separate to infinite separation); therefore, the 2 charges are bounded to each other. If 2 charges repel each other, their electric potential energy at each point is positive; the 2 charges are not bounded to each other.

For 26.a, you're right, I overlooked the r^2 in the denominator.

For 74, I'm confident in my sum. There are six pairs for a four-charge system.

What about 34? Are they wanting an actual value or expression? I don't see how to get an actual value, but I'll take a look at the equations again.