Cours et Exercices

Considering the electrostatic field in a plane defined by its components in polar coordinates: Determine the equation of the field lines. Back to the list of electromagnetism corrected exercises

Considering a half sphere of center O, of radius R, uniformly charged on surface with the surface density σ. 1. Determine the electrostatic potential at a point M of the axis Oz of symmetry of this hemisphere. 2. Deduce the expression of the electrostatic field at that point Mr. 3. Determine the potential and the electrostatic field on O. ( think for limited development). ► See the solution ► Back to the list of electromagnetism exercises

∎ Back to exercise   1. Research of the potential.   Consider a surface element of the half sphere centered at a point P. The electrostatic potential created at a point M of the axis Oz is expressed as: By integration over the azimuthal angle and expressing r:    and : Can then be expressed: The potential M is then: 2. Electrostatic field at M     We have : 3. Potential and field on O . The potential is written in the form: Calculating the boundary of V where z tends to 0: For the electric field, the procedure is the same way: ∎ 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 ~ ...