A particle of charge Q and mass m is released from origin at t=0 sec(as shown in the fig.) what will be the position of particle and direction at t=1 sec?

To determine the position and direction of a charged particle released from the origin at time t=0 seconds, we need to consider the forces acting on it and the resulting motion. The behavior of the particle will depend on the electric field in which it is placed, as well as any other forces that may be acting on it, such as gravitational force if applicable.

Understanding the Forces at Play

When a charged particle is placed in an electric field, it experiences a force given by Coulomb's law. The force \( F \) acting on the particle can be expressed as:

• F = Q * E

Here, \( Q \) is the charge of the particle, and \( E \) is the electric field strength. The direction of the force will depend on the sign of the charge and the direction of the electric field.

Analyzing the Motion

Once the force is known, we can determine the acceleration \( a \) of the particle using Newton's second law:

• a = F/m

Substituting the expression for force, we get:

• a = (Q * E) / m

This acceleration will dictate how the particle moves over time. If the particle starts from rest, its position at any time \( t \) can be calculated using the kinematic equation:

• x(t) = x_0 + v_0 * t + (1/2) * a * t^2

Since the particle is released from the origin, \( x_0 = 0 \) and \( v_0 = 0 \). Thus, the equation simplifies to:

• x(t) = (1/2) * a * t^2

Calculating the Position at t=1 Second

Now, substituting \( t = 1 \) second into the equation, we find:

• x(1) = (1/2) * a * (1)^2 = (1/2) * a

To find the exact position, we need the value of the acceleration \( a \). If we know the electric field \( E \), we can calculate \( a \) using the earlier formula. For example, if \( E = 10 \, \text{N/C} \), and \( Q = 1 \, \text{C} \), and \( m = 1 \, \text{kg} \), then:

• a = (1 * 10) / 1 = 10 \, \text{m/s}^2

Substituting this back, we get:

• x(1) = (1/2) * 10 = 5 \, \text{m}

Direction of the Particle

The direction of the particle's motion will be along the direction of the electric field. If the electric field points to the right, the particle will also move to the right. Conversely, if the electric field points to the left, the particle will move in that direction. The sign of the charge \( Q \) will also affect the direction; a positive charge moves in the direction of the field, while a negative charge moves opposite to it.

Final Thoughts

In summary, to find the position of the particle at \( t = 1 \) second, you need to calculate the acceleration based on the electric field and charge, then use that to find the position. The direction will depend on the charge's sign and the electric field's orientation. If you have specific values for \( Q \), \( m \), and \( E \), you can plug those into the equations to get a precise answer.