1-What is the shape of the trajectory of a charged particle moving in a uniform electric field if its initial velocity is null?
2-What is the shape of the trajectory of a charged particle moving in a uniform electric field if its initial velocity is perpendicular to the field?
3-What is the expression of the acceleration of a charged particle of mass m and charge q moving between two parallel plates a distance d apart between which a potential difference U is applied?
1- If a charged particle has an initial velocity of null (zero), and it is moving in a uniform electric field, the shape of its trajectory will be a straight line parallel to the electric field lines. The particle will experience an acceleration due to the electric field, but since it has no initial velocity, it will not deviate from its initial position.
2- If a charged particle has an initial velocity that is perpendicular to the electric field, the shape of its trajectory will be a parabolic curve. The particle will experience a constant acceleration due to the electric field, causing it to curve in a parabolic path.
3- The expression for the acceleration (a) of a charged particle with mass (m) and charge (q) moving between two parallel plates, separated by a distance (d), and a potential difference (U) applied is given by the equation:
a = qU / md
This equation is derived from the principle that the electric field between the plates is uniform, and the acceleration experienced by the particle is directly proportional to the potential difference (U) and inversely proportional to the mass (m) and the distance between the plates (d).
1- If a charged particle has a null (zero) initial velocity and is placed in a uniform electric field, its trajectory will be a straight line parallel to the direction of the electric field. This is because when the initial velocity is zero, there is no force acting on the particle to change its direction.
To understand this, you can use the equation of motion for a charged particle in an electric field: F = qE, where F is the force, q is the charge of the particle, and E is the electric field. Since the particle has no initial velocity (v = 0), the acceleration (a) is also zero. Therefore, according to Newton's second law (F = ma), the force acting on the particle is zero.
In a uniform electric field, the electric field lines are parallel, so the electric force on the charged particle will also be parallel to the electric field lines. Consequently, the particle will move along a straight line in the same direction as the electric field lines.
2- If a charged particle has an initial velocity perpendicular to a uniform electric field, its trajectory will be a curved path called a parabola. This is because the electric field exerts a force on the moving charged particle and causes it to accelerate in a direction perpendicular to both the electric field and its velocity.
To determine the shape of the trajectory, you can use the equation for the force on a charged particle in an electric field: F = qE, where F is the force, q is the charge of the particle, and E is the electric field. The force will always be perpendicular to the velocity due to the cross product between the velocity and the field. This perpendicular force causes the charged particle to change direction, resulting in a curved path.
The trajectory of the charged particle will be a parabola because the force acting on the particle is constant in magnitude and always perpendicular to the velocity. This corresponds to the motion of a projectile accelerated by a constant force, resulting in a parabolic path.
3- The expression for the acceleration of a charged particle moving between two parallel plates with a potential difference applied can be derived using the principles of electrostatics.
The electric field (E) between the plates is given by E = V/d, where V is the potential difference and d is the distance between the plates.
The electric force (F) on a charged particle in this electric field can be calculated using the equation F = qE, where q is the charge of the particle.
Since force is equal to mass times acceleration (F = ma), we can equate the two expressions:
qE = ma
Rearranging the equation, we get:
a = (qE) / m
Therefore, the expression for the acceleration (a) of a charged particle with mass (m) and charge (q) moving between two parallel plates with a potential difference (V) applied can be written as:
a = (q(V/d)) / m