A 10 μC charge of mass 20 g, initially at rest at x = - 1 m in a constant electric
field E = 2000 V/m is released from rest. What is its speed at x = 5 m?
To find the speed of the charge at x = 5 m, we can follow these steps:
Step 1: Calculate the work done on the charge.
The work done on a charge (W) is given by the equation:
W = q * ΔV
where q is the charge and ΔV is the change in electric potential.
In this case, the charge (q) is 10 μC (10 * 10^-6 C), and the change in electric potential across the distance of 5 m can be calculated using the formula:
ΔV = E * Δx
where E is the electric field and Δx is the change in position.
Using the given values, we can calculate ΔV:
ΔV = (2000 V/m) * (5 m)
ΔV = 10,000 V
Now, we can calculate the work done:
W = (10 * 10^-6 C) * (10,000 V)
W = 0.1 J (Joules)
Step 2: Calculate the change in kinetic energy.
The work done on the charge is equal to the change in kinetic energy (KE). Therefore:
W = ΔKE
ΔKE = 0.1 J
Step 3: Calculate the speed at x = 5 m.
The change in kinetic energy (ΔKE) is related to the mass (m) and the speed (v) of the charge by the equation:
ΔKE = (1/2) * m * (v^2)
Rearranging the equation, we can solve for v:
v^2 = (2 * ΔKE) / m
v = sqrt((2 * ΔKE) / m)
Substituting the given values:
v = sqrt((2 * 0.1 J) / 0.02 kg)
v = sqrt(10 J/kg)
v ≈ 3.16 m/s
Therefore, the speed of the charge at x = 5 m is approximately 3.16 m/s.