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. Imagine a small metal ball of mass m and negative charge -q0. The ball is released from rest at the point (0, 0, d) and constrained to move along the z-axis, with no damping. If 0 < d << a, what will be the ball's subsequent trajectory?A. repelled from the originB. attracted toward the origin and coming to restC.oscillatingalong the z-axis between z = d and z = -d.D. circling around the z-axis at z =d

FREE Expert Solution

Electric force:

F=kq1q2r2

Newton's second law:

F=ma

q = -q0 

E = kqz/(z2 + a2)(3/2)

F = -kqq0z/(z2 + a2)(3/2) 

at a point z = d,

F = -kqq0d/(d2 + a2)(3/2) 

When d << a, (d2 + a2) is approximately equal to a2 

F = -kqq0d/a3 = (-kqq0/a3)d 

View Complete Written Solution
Problem Details

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. 

Imagine a small metal ball of mass m and negative charge -q0. The ball is released from rest at the point (0, 0, d) and constrained to move along the z-axis, with no damping. If 0 < d << a, what will be the ball's subsequent trajectory?

A. repelled from the origin

B. attracted toward the origin and coming to rest

C.oscillatingalong the z-axis between z = d and z = -d.

D. circling around the z-axis at z =d

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Coulomb's Law with Calculus concept. You can view video lessons to learn Coulomb's Law with Calculus. Or if you need more Coulomb's Law with Calculus practice, you can also practice Coulomb's Law with Calculus practice problems.