Exercise Pro

∎ 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 ~ ∎ ( The solution ) ∎ 4. Field Lines ►See the list of electromagnetic corrected exercises

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

∎ Back to exercise     Consider a surface element S on the truncated cone centered about the point P. The Elemental electrostatic potential created at the point O of the axis Ox by a surface element dS centered about the point P is expressed as: so : We get :   By integration: We get : ∎ Back to exercise ∎ Back to the list of electromagnetism corrected 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

∎ 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  

∎ 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 ) ►See the list of electromagnetic corrected exercises

►Back to exercise Field at the center of a loaded ring having an opening. And the xOy plane xOz are planes of symmetry of the distribution of loads, the electrostatic field must belong simultaneously to these two planes, so they intersect. The field at the point O is then carried by the right Ox. Either elemental electrostatic field created by the length dl element centered at a point P on the charged circumference of the ring: Given the symmetry of the charge distribution, only the component along Ox contributes to total field O. Where: The resulting field component for O: ►Back to exercise ►See the list of exercises

► See solution A ring center O and radius R bears a uniform linear charge density λ except on a corner arc center 2α Determine the electrostatic field in O. ► See solution ►See the list of electromagnetism exercises