A sphere has a net charge of 8.03 nC, and a negatively charged rod has a charge of −6.05 nC.
The sphere and the rod undergo a process such that 5.40 ✕ 109 electrons are transferred from the rod to the sphere. What are the charges of the sphere and the rod after this process?
To find the charges of the sphere and the rod after the process, you need to consider the charge transferred from the rod to the sphere.
Given:
Net charge of the sphere = 8.03 nC
Charge of the rod = -6.05 nC
No. of electrons transferred = 5.40 x 10^9
To determine the new charge, you should calculate the charge transferred, assuming each electron carries a charge of 1.6 x 10^-19 C.
Charge transferred = No. of electrons transferred × charge per electron
Charge transferred = 5.40 x 10^9 × 1.6 x 10^-19
Now, let's calculate the charge transferred:
Charge transferred = 8.64 x 10^-10 C
Since the electrons are transferred from the rod to the sphere, the charge on the rod decreases by the amount transferred, and the charge on the sphere increases by the same amount.
To find the new charge on the rod:
Charge of the rod after transfer = Initial charge of the rod - Charge transferred
Charge of the rod after transfer = -6.05 nC - (-8.64 x 10^-10 C)
Now, let's calculate the charge on the rod after the transfer:
Charge of the rod after transfer = -6.05×10^-9 C + 8.64x10^-10C
Charge of the rod after transfer ≈ -5.19 nC
To find the new charge on the sphere:
Charge of the sphere after transfer = Initial charge of the sphere + Charge transferred
Charge of the sphere after transfer = 8.03 nC + 8.64 x 10^-10 C
Now, let's calculate the charge on the sphere after the transfer:
Charge of the sphere after transfer = 8.03×10^-9 C + 8.64×10^-10 C
Charge of the sphere after transfer ≈ 8.89 nC
Therefore, after the process, the charge on the rod is approximately -5.19 nC, and the charge on the sphere is approximately 8.89 nC.