A particle, with mass m and charge q, was placed at a point A of an electric field where the vector of the electric field is vertical, pointing upwards and has magnitude E. If we know E, m, and g (free-fall acceleration), determine:
a) The charge q, knowing that the particle is in equilibrium at point A;
b) The sign of the electric charge.

Problem data:

• Mass of the particle:    m;
• Magnitude of the electric field:    E;
• Free-fall acceleration:    g.

Problem diagram:


Solution

a) In the particle acts the weight \( \vec{W} \), due to the action of gravity, and the electric force \( {\vec{F}}_{E} \), due to the electric field. As the weight acts in the vertical downwards, the electric field should produce an electric force vertically upwards, of the same magnitude. So the particle is in equilibrium, we have the following condition the electric force is given by and the weight is given by equating these two expressions, we have
b) As electric force has the same direction as the electric field the particle is positive.