12. A charge Q is distributed evenly on a wire bent into an arc of radius R , an

Question

12. A charge Q is distributed evenly on a wire bent into an arc of radius R, and subtending an angle , as shown in the figure. Determine the electric field at the center, O, of the arc as a function of the angle .

13. Three charges, q1, q2, and q3, are located at the corners of an equilateral triangle with side length of 1.2 m. Find the work done in each of the following cases: (a) (2 pts) to bring the first particle,

q1 =1.0 pC, to P from infinity; (b) (3 pts) to bring the second

particle, q2 = 2.0 pC, to Q from infinity; (c) (3 pts) to bring the last particle, q3 =3.0 pC, to R from infinity. (d) (2 pts) Find the total potential energy stored in the final configuration of q1, q2, and q3.

14. The circuit shown in the figure at right consists of two batteries with VA and VB and three light bulbs with resistances R1, R2, and R3.

(a) (6 pts) Calculate algebraically the magnitudes of the currents i1, i2, and i3 flowing through the bulbs. (b) (2 pts)

NOTE: EMAIL ME IF YOU WANT THE IMAGES TO SOLVE THIS PROBLEMS AT TEAM_GAME@YAHOO.COM

Explanation / Answer

here,

The radial differential Electric field at the center

dEx = (1/4o)*dq/R^2*cos()

where
dq = *R*d
where is the charge distribution = Q/R*

Now integrate dEx from - to +

Note : theta is the half angle of the arc

so

E = (1/4o)*/R*(-sin() - sin(-)) but sin(-)

E = -sin()

so E = 2* (1/4o)*/R*sin()

but = Q/R*

so

E = 2* (1/4o)*Q/R^2*(sin()/)

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