A particle with a charge of -5.0 μC and a mass of 4.3 x 10-6 kg is released from rest at point A and accelerates toward point B, arriving there with a speed of 18 m/s. The only force acting on the particle is the electric force. What is the potential difference VB - VA between A and B? If VB is greater than VA, then give the answer as a positive number. If VB is less than VA, then give the answer as a negative number.
To find the potential difference (VB - VA) between points A and B, we can use the equation:
VB - VA = q(Electric potential at B) - q(Electric potential at A)
First, we need to find the electric potential at point A and point B.
The electric potential at a point depends on the distance from the charged particle. Since we do not have information about the positions of A and B, we need to approach this problem in a different way.
We are given that the particle is released from rest at point A and arrives at point B with a speed of 18 m/s. This means that the particle gained kinetic energy while moving from A to B.
The electric force acting on the particle is conservative. Therefore, the work done by the electric force on the particle is equal to the change in its potential energy.
The potential energy (U) of a charged particle due to the electric field is given by the equation:
U = q * V
Where q is the charge of the particle and V is the electric potential.
The change in potential energy (ΔU) is given by:
ΔU = U(B) - U(A) = q * (VB - VA)
Since the particle gains kinetic energy, the change in potential energy is negative. Therefore:
-ΔU = -q * (VB - VA)
The work done by the electric force is equal to -ΔU. By using the work-energy theorem, we can write:
Work done by electric force = Change in kinetic energy
Therefore:
-ΔU = -q * (VB - VA) = K(final) - K(initial)
Where K is the kinetic energy of the particle.
The initial kinetic energy (K(initial)) is zero as the particle was released from rest.
We can calculate the final kinetic energy (K(final)) using the mass of the particle and its speed at point B:
K(final) = (1/2) * m * v^2
Plugging in the values, we get:
K(final) = (1/2) * (4.3 x 10^-6 kg) * (18 m/s)^2
Now, we can solve for the potential difference (VB - VA):
-q * (VB - VA) = K(final) - K(initial)
Since K(initial) is zero:
-q * (VB - VA) = K(final)
Plugging in the known values:
-(-5.0 μC) * (VB - VA) = (1/2) * (4.3 x 10^-6 kg) * (18 m/s)^2
Simplifying this equation will give us the potential difference (VB - VA) between points A and B. Remember to consider the sign (positive or negative) based on whether VB is greater or smaller than VA.