#4 (a) At what position x is the third bead in equilibrium? (b) Can the equilibr

Question

#4

(a) At what position x is the third bead in equilibrium? (b) Can the equilibrium be stable? 4. Two charged particles are located on the x axis. The first is a charge +Qat x-a. 1 second is an unknown charge located at x = +3a. The net electric field these charges produce at the origin has a magnitude of 2kQ/a. What are the two possible values unknown charge? 5. A uniformly charged ring of radius 10.0 cm has a total charge of 95.0 pC. Find the electric field on the axis of the ring at the following distances from the center of the (a) 1.00 cm, (b) 5.00 cm, (c) 30.0 cm (d) 100 cm, 6. The figure below shows the electric field lines for two charged particles separated small distance.

Explanation / Answer

electric field due to charge 1

E1x = k*Q/a^2

electric field due to charge 2 ( unknown)

Q2 can be negative or positive

if Q2 is negative

E2x = k*Q2/(3a)^2 = k*Q2/9a^2

net electric field

E = E1x + E2x

2*k*Q/a^2 = k*Q/a^2 + k*Q2/(9a^2)

2Q = Q + Q2/9

Q2 = 9Q

charge Q2 = -9Q

if Q is posituve

E2x = -k*Q2/(9a^2)

Ex = -k*Q/a^2

-2*k*Q/a^2 = k*Q/a^2 - k*Q2/(9a^2)

-2Q = Q - Q2/9

Q2 = 27*Q

charge Q2 = -Q or +27Q

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