Question

Consider four charges q, −q, q, −q fixed on the x-axis at x = −3a, −a, a, 3a respectively.

I) Find a point(s) on the y-axis at which the electric field is zero.
II) Find a point(s) on the x-axis at which the electric field is zero.
III) Find the frequency of small oscillation for a test particle around the point of equilibrium in II. What is the sign of the test particle exhibiting small oscillation?
IV) Find the energy needed to assemble the configuration.
V) A particle of mass m and charge q is released from rest at x = 4a. Find its velocity as it reaches a far point.

Answer 1

I) There are no points on the y-axis where the electric field is zero.
II) The electric field is zero at the midpoint between the pairs of opposite charges, which is at x = 0.
III) The frequency of small oscillation for a test particle around the point of equilibrium at x = 0 can be found using the formula for simple harmonic motion.
IV) The energy needed to assemble the configuration can be calculated by summing up the potential energy contributions from each pair of charges.
V) The velocity of the particle as it reaches a far point can be determined using the conservation of energy, equating the initial potential energy to the final kinetic energy.