Chapter 1

# To test the understanding of the lesson

## Question

• What is the potential electrostatic interaction energy of a charge placed at a point where an electric potential exists ?

• What is the potential electrostatic interaction energy of charges , placed at points where an electric potential exists ?

### Solution

• The potential electrostatic energy of a charge placed at a point where exists an electric potential is :

• The potential electrostatic energy of charges placed at points where exists a potential  is :

## Question

Define the .

### Solution

The is an energy unit. It is the kinetic energy gained by an electron which was accelerated by a voltage difference . Thus :

## Question

• What is the potential electrostatic interaction energy of an electric dipole, which has a dipole moment vector surrounded by an exterior uniform field  ?

• What is the potential magnetic interaction energy of a magnetic dipole, which has a magnetic moment vector surrounded by an exterior uniform magnetic field  ?

### Solution

• The potential electrostatic interaction energy of an electric dipole, which has a dipole moment vector surrounded by an exterior uniform field is :

• The potential magnetic interaction energy of a magnetic dipole, which has a magnetic moment vector surrounded by an exterior uniform magnetic field is :

## Question

• Define the electric dipole moment of a set of two charges in P and in N.

• Define the magnetic moment of a circuit crossed by an intensity . What if the circuit is a circular loop of radius ?

### Solution

• The dipole moment is expressed by :

• The magnetic moment is :

Where is the circuit surface and the normal vector of the oriented circuit (obtained with the Right-hand rule).

For a circular loop whose normal axis is (Oz) for example :

## Question

• What is the expression of a potential created by a dipole, under the dipole approximation ?

• Deduce the electric field created by the dipole.

### Solution

• The potential created by the dipole is :

• The electric field is given by :

## Question

• Quote Gauss' law.

• Quote Ampère's circuital law.

### Solution

• Gauss' law :

• Ampère's circuital law :

## Question

Eight identical spherical drops of mercury are charged to a voltage equal to .

What will be the voltage of the big drop obtained after the fusion of these drops ?

### Solution

The charge of the initial drop is , with and each drop has a radius equal to .

The big drop has the same volume as the sum of the eight others. Thus its radius is :

Consequently :

Hence the final potential is expressed by :

## Question

A nucleus of Neon is accelerated by a voltage difference equal to .

Find its velocity, considering that the atomic mass of Neon is equal to and its number in the periodic table is .

The mass of a proton is .

### Solution

Energy conservation law gives :

Here, ( is the charge of an electron) and is equal to times the mass of a proton.

Thus :

.

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