VirtualDynamics UniversitySolved UniversityPhysics ProblemsPhysics 3: Introduction to Electricity & Magnetism <<< Electric Field, Potential and Potential Difference >>>Javier Montenegro Joo jmj@VirtualDynamics.OrgReturn to Electricity and Magnetism Index page Return to VirtualDynamics University home page

<<< Electric Field, Potential and Potential Difference >>> 
(1) Two parallel plates of
length L and separation d, (L>>d) have opposite charges so that there is
a vertical electric field and a potential difference Vo, between them.
A particle of mass m, charge Q and horizontal velocity V_{ox}
enters the region between the plates, at the level of the positive
plate. Neglecting the effect of the acceleration of the gravity,
determine the vertical position of the particle, when it has traveled a
horizontal distance equal to half the separation between the plates. Solution. The electric field between the parallel plates accelerates upwards the positively charged particle. As a consequence of the combined effects of the horizontal velocity of the particle and the vertical acceleration, the particle displaces along an upward parabolic trajectory between the plates.

(2)
Between two vertical charged parallel plates exists a uniform electric
field. Inside the field there is a particle of mass m and charge Q,
displacing with velocity v_{o} Determine (a) The
potential difference to be applied in order to reduce in 20% the
speed of the particle (b) The change in the kinetic energy of the
particle.
Solution Any work made on a particle produces in a change in its kinetic energy. A force applied along a distance ‘d’ is work: W = F d and work is energy. Reducing the speed of a particle is equivalent to decelerate it and to reduce its kinetic energy. In order to decelerate a positive electric charge, a negative potential must be applied.

(3) Consider a spherical distribution of electric charge expressed by
For an outer radial distance r, determine the electric field and the electric potential. Solution.

EduVirtualLab: Aplicación del Decremento Logarítmico para identificar parámetros de una oscilacion. 
(4) A spherical shell made of conductive material, with radiuses ‘a’ and ‘b’, (a < b), has an electrical charge density of 10 Qo/3. For points outside the shell, compute (a) Electric field (b) electric potential. Solution. Since the shell is made of conductive material, the electric charge distributes only on its surface, hence the mentioned density is superficial. At the time of calculating the electric potential it must be borne in mind that very far from the shell (at the infinite), the effect of its electrical charge (its potential) is null.

(5) Two very long cylindrical and concentric shells, made of metal, with radiuses r1 and r2, (r1 < r2), possess charge densities Lambda and –Lambda, respectively. It is observed that at a distance r0, such that r0 > r2, the electric potential is zero. Determine the potential difference between the cylindrical shells. Solution. Note that in this system of two oppositely charged concentric cylinders the total electric charge is null, because positive and negative charges of equal magnitude cancel each other. In the region inside r1 there is no charge. Then there is no electric field, neither in the outer region of the cylinders, nor in their inner region. Electric field exists only in the region between both cylinders and, this field is due only to the charge in the inner shell. The charge of the outer cylinder does not contribute to the electric field between both shells.

Algorithmic Art images by JMJ: http://www.virtualdynamicssoft.com/virtualdynamicsart_e.htm 
(6)
Four electric
charges, 3Q_{o }, 6Q_{o }, 9Q_{o } and
Q, are placed each in a corner of a square of side 2L. Determine:
(a) The charge Q so that the electric potential at the center of the
square is zero. (b) The total electric field at the center of the
square.
Solution.

(7) In
the figure, a wire has been bent so that it has the shape of a
semicircumference of radius R, then the wire has been loaded with an
electric charge and, this distributes as a linear density L=LoSin(Theta). Determine the
electric potential at the origin of coordinates.
Solution.
