(a) Write two properties by which electric potential is related to the electric field. (b) Two point charges q1 and q2 , separated by a distance of r12 are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in the field.

A rod of length L = 4.00 m with uniform charge of 9.50 nC/m is oriented along the y axis as shown in the diagram. P, (a) What is the electric potential at the location P1 whose coordinates are (0, -6.00 m)? V (b) What is the electric potential at the location P2 whose coordinates are (6.00 m, 2.00 m)?

A square of side a = 1 m has charges +Q and -Q (Q = 2 μC) alternating from one corner tothe next. Find the electric potential energy for the systems of charges.

Consider two points in an electric field. The potential at point 1, V1, is 21 V. The potential at point 2, V2, is 159 V. An electron at rest at point 1 is accelerated by the electric field to point 2. Part (a)  Find the change of the electric potential energy of the electron, in electron volts (eV).  Part (b)  Find the speed of the electron at point 2, v2, in meters per second.

Two protons are located at (2.00, 0) m and (0, 2.30) m, respectively. Determine the following. (a) the electric potential at the origin V (b) the electric potential energy of a third proton located at the origin J

A point charge Q1=+5.9 uC is fixed in space, while a point charge Q2=+2.2 nC, with mass 7.6 ug, is free to move nearby. A) calculate the electric potential energy of the system, in joules, when Q2 is located 0.42 m from Q1. B) if Q2 is released from rest at a point 0.42 m from Q1, what will be its speed, in meters per second, when it is 0.77m from Q1? 

Three charged particles are located on x-axis. Particle 1 carries charge +2 nC, located at x = -3 cm; particle 2 carries charge -3 nC, located at x = 1 cm; particle 3 carries charge +1 nC, located at x = 5 cm. Calculate the electric potential energy of particle 3. Answer should be in Joules

Four objects with positive charges of +1.0 x 10-5 C are placed at the four vertices of a45° rhombus with sides of length 2.0 m.(a) Calculate the electric potential at the centre of the rhombus (this is located where thediagonals intersect). b) Calculate the electric potential energy a charge of +3.0 x 10-5 C would have if placed atthe centre of the rhombus.

An electron is placed in an xy plane where the electric potential depends on x and y as shown in the figure (the potential does not depend on z). The scale of the vertical axes is set by Vs = 500 V. In unit-vector notation, what is the electric force on the electron? Number i V (V) -V₁ i i 0.2 x (m) 0.4 V (V) S _V₂ 0.2 y (m) j Units 0.4 <

Consider the system below with two charges, each equal to + 2.90µC, placed 0.06 m apart. a) Find the total electric field (both magnitude and direction) at point Plocated 0.04 m away from q1. Draw two arrows at that point in the figure to show the directions of the electric fields due to q1 and q2. b) Find the electric potential of the system at P. c) Find the electric potential energy of the system and comment if it isstable.