A moving particle encounters an external electric field that decreases its kinetic energy from 9100 eV to 6630 eV as the particle moves from position A to position B. The electric potential at A is -59.5 V, and the electric potential at B is +26.1 V. Determine the charge of the particle.
To determine the charge of the particle, we need to use the relationship between electric potential (V), charge (q), and kinetic energy (KE), which is given by:
KE = qV
We can rearrange this equation to solve for the charge (q):
q = KE / V
First, we need to calculate the change in electric potential (ΔV) between positions A and B:
ΔV = Vb - Va
ΔV = +26.1 V - (-59.5 V)
ΔV = 85.6 V
Next, we need to calculate the change in kinetic energy (ΔKE) of the particle:
ΔKE = KEb - KEa
ΔKE = 6630 eV - 9100 eV
ΔKE = -2470 eV
Now, we can calculate the charge (q) using the equation q = ΔKE / ΔV:
q = (-2470 eV) / (85.6 V)
However, we need to convert eV to coulombs (C) in order to obtain the charge in the SI unit. We can use the conversion factor 1 eV = 1.602 x 10^-19 C:
q = (-2470 eV) / (85.6 V) * (1.602 x 10^-19 C / 1 eV)
Calculating this, we get:
q ≈ -8.96 x 10^-19 C
Therefore, the charge of the particle is approximately -8.96 x 10^-19 Coulombs.