Consider a uniformly charged ring in the xy plane,...

Question

Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference.

What is the magnitude of the electric field along the positive z axis?

Use k in your answer where:

$k = \frac{1}{4 {πε}_{0}}$

E(x) = ______

Patrick Ford · Accepted Answer

Electric filed:E=kqr2Consider a point with the point z, located on the positive z-axis. The ring has a radius a. An electric field vector originating from an element of charge on the ring makes an angle θ with the z-axis.The adjacent side has a length z, the opposite side has a length a and the hypotenuse is equal to (z2 + a2)(1/2). The net electric field is directed along the z-axis. [readmore]Therefore, its direction is given by cos θ = adjacent/hypotenuse = z/(z2 + a2)(1/2).The distance from a point charge on the ring to the point z is equal to the hypotenuse, (z2 + a2)(1/2).r2 = [(z2 + a2)(1/2)]2 = z2 + a2Ez = kq/r2 cosθ = kq/(z2 + a2)•z/(z2 + a2)(1/2) = kqz/(z2 + a2)(3/2) The electric field at a point z on the positive z-axis is equal to kqz/(z2 + a2)(3/2)

Problem: Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. What is the magnitude of the electric field along the positive z axis?Use k in your answer where:k=14πε0E(x) = ______

FREE Expert Solution

Problem Details

Problem: Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. What is the magnitude of the electric field along the positive z axis?Use k in your answer where:k=14πε0E(x) = ______

FREE Expert Solution

Problem Details

Sign up for free to watch this video!