StephenDoty said:from pi/2 to 2pi
meaning the test particle would go up and to the right.
as I drew the lines of E I couldn't tell how any component could cancel, and if you spit it up neither the x or y component cancel out as the r's are different. If the rod was a half circle the y's would cancel out but if it is just a 1/4 circle there is an x- and y-components, thus for a 3/4 circle there would be x- y- components.
A uniformly charged rod in an arc is a physical system in which a long, thin rod is bent into a circular shape and has a uniform distribution of electric charge along its length.
The electric field at a point on the axis of a uniformly charged rod in an arc is given by the formula E = (kQx) / (x^2 + R^2)^3/2, where k is the Coulomb's constant, Q is the total charge on the rod, x is the distance from the center of the arc to the point, and R is the radius of the arc.
The electric potential at a point on the axis of a uniformly charged rod in an arc is given by the formula V = (kQ) / (x^2 + R^2)^1/2, where k is the Coulomb's constant, Q is the total charge on the rod, x is the distance from the center of the arc to the point, and R is the radius of the arc.
As you move along the axis of a uniformly charged rod in an arc, the electric field and potential will decrease as the distance from the rod increases. This is because the electric field and potential are inversely proportional to the distance from the charge.
The electric field and potential of a uniformly charged rod in an arc will be affected by the material it is made of. Different materials have different dielectric constants, which will affect the electric field and potential. In general, materials with higher dielectric constants will result in stronger electric fields and potentials.