Positive charge Q is distributed uniformly along a rod of length L that lies along the x-axis from x=L to x=2L.   (a) How much charge is contained within a segment of the rod of length dx? Express your answer in terms of the variables Q, L, and dx.   (b) Integrate to find the total electric potential at the origin (x=0) due to the rod. Express your answer in terms of the electric constant ϵ0 and variables Q, L.

A plastic rod has been bent into a circle of radius R = 11.0 cm. It has a charge Q1 = + 5.38 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference (see the figure). With V = 0 at infinity, what is the electric potential (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D = 6.02 cm from the center?

Suppose that the electric potential V in a certain region is given by V (x, y, z) = Ax – B (y – z²) where A and B are constants. Find expressions for the components of the electric field in this region. %3D E, = E =

A uniform electric field exists in the region between two oppositely charged parallel plates. The electric field has a magnitude of 5.49 × 10³ N/C. The plates are separated by 0.500 cm. The potential difference between the two plates is V. Express your answer in normal format and 3 SF.

A point charge of 1 μC is located at the origin, which is the center of a thin spherical shell of 10 cm radius. This shell is uniformly charged with 17 μC. What is the electric field at r=5 cm and r=15?E1 =  V/m,E2=  V/m.What is the electric potential at these points?V1 =  V,V2=  V.

A semicircle of radius R has charge lining its outer edge, with a charge +q uniformly distributed on one half and a charge -q uniformly distributed on the other half. The point P is located at the center of circle that describes this semicircle. At point P, find (a) the electric field. (b) the electric potential.

A uniform electric field exists in the region between two oppositely charged parallel plates. The electric field has a magnitude of 6.31 x 10³ N/C. The plates are separated by 0.500 cm. The potential difference between the two plates is V. Express your answer in normal format and 3 SF.

Consider a ring of charge in the x-y plane of radius 2.7 m, centered at the origin.  The charge per angle around the ring is given by dQ/dα = a (1 - cos α)  (nC/rad), where a = 8.4 nC/rad.  Calculate the electric potential along the z axis at z = 5.8 m, in V.  Use k = 9 x 109 N m2 / C2. (Please answer to the fourth decimal place - i.e 14.3225)

A plastic rod has been bent into a circle of radius R = 5.03 cm. It has a charge Q, = +7.42 pC uniformly distributed along one-quarter of its circumference and a charge Q, distributed along the rest of the circumference (see the figure). With V = 0 at infinity, what is the electric potential (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D = 6.91 cm from the center? -6Q1 uniformly P, Q2 R (a) Number Units (b) Number Units Click if you would lik

A positive charge is evenly distributed on the surface of a metal sphere centered at the origin of the coordinate system. The positive charge produces an electric field that points outwardly in the radial direction. A positive test charge is fixed at a distance R₁ from the center of the coordinate system, far from the surface of the sphere. The electric potential at R₁ is 10V. The positive test charge is then allowed to move freely until it reaches a distance R₂=2R₁ from the center of the coordinate system. What is the electric potential (in Volts) of the test charge at its new resting point? 10