Cours et Exercices

Consider a disk its center O and its radius R. This system is loaded on the surface with the surface density:   a is a constant homogeneous to a length and r is the distance of a point P on the surface of the disc to its center . Determine the electrostatic potential at a point M of the axis  of revolution Oz of this disc. For the calculation is carried out the change of variable r = z u sh. Deduce the expression of the electrostatic field in point M. ► See the solution ► Back to the exercises of electromagnetism list  

∎ Back to exercise 1. The potential at a point M of the axis. Consider a surface area element of the disk centered at a point P. The electrostatic potential created at a point M of the axis Oz is expressed as: Since r and θ variables are separated : For the calculation is performed following variable change: For : On the other hand : We get : Taking the zero potential at infinity is obtained: 2. Field at a point M of the axis. The z axis is axis of symmetry of the charge distribution. The field at a point M of the axis is carried by this axis: We must therefore calculate the derivative of the function . We have: x = y where sh As   ∎ Back to exercise ∎ Back to the list of electromagnetism exercises

► E lectrostatic field . ► 1. Field the center of a ring having an opening. ~  ► (The solution ) ► 2. Field created by a hemisphere surface   charge . ~   ► ( The Solution )   ► 3. field created by a portion of a cone . ~   ► (The Solution ) ► 4. Field created by a disc at a point on its axis. ~    ► (The Solution )   ► 5. electrostatic field created by an electrified segment. ~   ► (The solution )   ► 6. Electrostatic field created by a hemisphere surface charge. ~   ► ( The solution )   ► 7. Electric field on the axis of a system (-q, + q) ~   ► ( the solution )     ►2. Electrostatic potential . ∎ 1. The potential field created by a disc at a point on its axis of revolution . ~ ∎ ( The Solution )   ∎ 2. Potential and field created by a charged hemisphere surface ~ ∎ ( the solution ) ∎ 3. The potential created by a portion of a cone ~ ...