A charge Q = -610 nC is uniformly distributed on a ring of 2.4-m radius.A point charge is fixed at the center of the ring,as shown in the figure.An electron is projected from infinity toward the ring along the axis of the ring.This electron comes to a momentary halt at a point on the axis that is 5.0 m from the center of the ring.What is the initial speed of the electron at infinity? ,k = 1/4πε₀= ,m_el= A) 6.6 × 10⁶ m/s B) 4.5 × 10⁶ m/s C) 3.4 × 10⁶ m/s D) 2.2 × 10⁶ m/s E) 1.1 × 10⁶ m/s

Question

Quizplus · Accepted Answer

To solve this problem, we can use conservation of energy:

Initial kinetic energy of the electron = Final gravitational potential energy of the electron + Final electric potential energy of the electron

At infinity, the electron has zero gravitational potential energy and zero electric potential energy (since it is infinitely far away from the charged ring and point charge). Therefore:

1/2 mv_inf^2 = kQq/r + kqQ/d

where m is the mass of the electron, v_inf is the initial speed of the electron at infinity, Q is the charge on the ring, q is the charge of the electron, r is the radius of the ring, d is the distance between the ring and point charge, and k is Coulomb's constant (1/4πε₀).

We can solve for v_inf:

v_inf = sqrt[2kQq/r + 2kqQ/d]/m

Substituting in the given values and solving, we get:

v_inf = 6.6 × 10^6 m/s

Therefore, the best choice is A.

A Charge Q = -610 NC Is Uniformly Distributed on a Ring