Question

Pixy) A dipole (equal positive and negative charges separated by a distance d) is centered on the origin along the y axis as shown in the figure. a. Redraw the figure with the appropriate distances (Ar+ and Ar.) between each charge and the arbitrary point P(x, y). b. Determine the distances Ar+ and Ar. in terms of d and x and y. c. Find V(x,y) d. Find Ex and Ey. e. Find Ē(x,y). Pxy) A line of uniform charge density and length d is along the y axis with one end at the origin, as shown in the figure. a. Redraw the figure with a small piece of charge da producing an electric potential dV at the location P(x,y). Include in this drawing the appropriate distance r between the infinitesimal piece of charge, dg, and the point P(x, y). b. Determine dq/r. Find the integral form for V. d. Solve for V(x,y). e. Determine Ex and Ey. f. Find Ē (x, y).

Answer 1

< det nje i obey A8+ = (52+(°)* - &*** ¢ Cose)" = 172 - rd cos@) K2 07. - 172+)2 + 2rd Coso)" - (+2+ + vd coso) V3,4)= VCEN) = vez de v $( c056) s = ('- Coso) ver) = kq (*) (*+ COSO - 1 + b (SC) le cos() = KP COSO P = 90 CS Scanned with CamScanner

(d) using gradient in polar Co-ordinates - ÉS.) = to the + b ) 3-KP ( 590 ) ** - KP 2 ( 8050) = QKP cose + Rp sino o 73 = KP ( acoso ř + sino o) 73 for x- axis > Év - KP (2Coso + Sino o) o = 90 2 for y-axis » 8 = 2KP i 33 KP 12 Coso ý + sino ôn) na ) È (ro): Scanned with CamScanner
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