To the right is a straight segment of constant linear charge density rho_1 runni

Question

To the right is a straight segment of constant linear charge density rho_1 running from a to b but shifted up a distance c above the plane, as shown. What is the position vector r to this charge segment assuming you wish to find the electric field using a Coulomb's law expression? Y' x cap + z z cap x' x cap y cap y cap + c z cap None of the others x' x cap + c z cap To the right is a straight segment of constant linear charge density rho_1 running from a to b but shifted up a distance c above the plane, as shown. What is the position vector r to the observation point shown assuming you wish to find the electric field using a Coulomb's law expression? (b - a) y cap + c z cap None of the others -c z cap c z cap (b - a) x cap + c z cap

Explanation / Answer

Solution:

(13) The charge segment lies in the Y-Z plane as clearly visible from the diagram. Now, the position vector is always determined in reference to the origin. So the position vector r' will have a representation of the form (0-0)ax+(y'-0)ay+(c-0)az. Therefor r'=y'ay+caz (Option c.) where ax, ay and az are respectively the unit vectors in the x, y and z directions. Also, y' will be equivalent y-coordinate of the linear charge distribution.

(14) The position vector of the observation point C lies on z-axis, hence r will have a representation of the form (0-0)ax+(0-0)ay+(c-0)az. Therefor r=caz (Option d.) where az is the unit vector z direction.

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