A circular line charge having radius \"R\" with a total charge of +Q lies on the

Question

A circular line charge having radius "R" with a total charge of +Q lies on the xy plane centered at the origin. A separate point charge of -2Q sits at the origin....

Please explain your work. Also please include your formulas/diagrams.

2 -20 A circular line charge having a radius 'R' with a total charge of+Q lies on the xy plane centered at the origin. A separate point charge of 2Q sits at the origin. 4. a) Find the magnitude and direction of the electric field (in general) at z b) Find the electric potential (in general) at z = a, y-0, x = 0. a, y 0, x 0

Explanation / Answer

4. (A) due to ring,

E1 = ( k Q / (R^2 + a^2)) (a / sqrt(R^2 + a^2))

E1 = k Q a / (R^2 + a^2)^(3/2)

due to point charge,

E2 = - k (2Q) / a^2 = - 2 k Q / a^2

E = E1 + E2

= k Q a / (R^2 + a^2)^(3/2) - 2 k Q / a^2

= (k Q ) [ a / (R^2 + a^2)^(3/2) - 2 / a^2]

magnitude = (k Q ) [ 2 / a^2 - a / (R^2 + a^2)^(3/2)]

direction = along z AXIS

(b) Potential,

V1 = k Q / sqrt(a^2 + R^2)

V2 = k(-2Q) / a

V = V1 + V2 = (k Q )[ 1 / sqrt(a^2 + R^2) - 2/a ]

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