Question

Two identical point charges, each of - 6.0 nC are held fixed on the x-axis, one at x= -3.0 cm, y =0, and the other at x = +3.0 cm, y= 0. In what follows, the electric potential is taken to be zero at infinity.

Calculate the electric potential VA at location A of coordinates x = 0, y= +4.0 cm, and the electric potential VB at location B of coordinates x = 0, y = 0 (the origin).

The proton is released from rest at location A and immediately starts moving along the y-axis towards location B. Use conservation of energy to calculate the speed of the proton when it reaches location B.

Answer 1

inal answer:

The question involves calculating the electric potentials at two points due to two identical negative point charges and using conservation of energy to determine a proton's speed as it moves from one point to the other.

Step-by-step explanation:

The question pertains to the calculation of electric potential and the conservation of energy principle to determine the speed of a proton. We are given two point charges, both of -6.0 nC, located symmetrically on the x-axis at points -3.0 cm and +3.0 cm. To find the electric potential at a location A with coordinates (0, +4.0 cm, 0) and at location B at the origin (0, 0, 0), we use the formula for the electric potential due to a point charge, V = kq/r, where V is the potential, k is Coulomb's constant, q is the charge, and r is the distance from the point charge to the point of interest.

To calculate the speed of a proton released from rest at location A moving towards B, we use the principle of conservation of energy. The proton's loss in electric potential energy equals its gain in kinetic energy since it starts from rest. The kinetic energy at location B can be expressed as (1/2)mv^2, where m is the mass of the proton and v is the final speed we aim to find.