Hi can someone please explain to me how to get the answers to the following questions. It would be greatly appreciated
A pair of horizontal parallel plates are placed a small distance, 4.00 mm, apart in air. Each plate is rectangular with a width of 20.0 cm, and length of 37.0 cm. The potential on the upper plate relative to the lower plate is 1.07 ¡Ñ 103 V.
a)What is the magnitude of the electric field between the plates?
b)A tiny drop of oil with an excess charge of ¡V1.31 ¡Ñ 10¡V17 C and mass of 4.00 ¡Ñ 10−6 kg is placed just above the lower plate. Calculate the magnitude of the electrical force it experiences.
c)Calculate the number of excess electrons on the oil drop.
d)The oil-drop is then released. What would be the kinetic energy of the drop when it arrived just below the upper plate, assuming that you were able to ignore non-electrical effects such as gravity?
Sure! I can help you with that. Let's go through each question step by step:
a) To find the magnitude of the electric field between the plates, you can use the formula:
Electric field (E) = Voltage (V) / Distance (d)
In this case, the voltage between the plates is given as 1.07 × 10^3 V, and the distance between the plates is 4.00 mm (or 0.004 m). Plugging these values into the equation, we get:
Electric field (E) = 1.07 × 10^3 V / 0.004 m
You can calculate this to find the answer.
b) To calculate the magnitude of the electrical force on the oil drop, you can use the equation:
Force (F) = Charge (q) × Electric field (E)
The charge on the oil drop is given as -1.31 × 10^-17 C (negative because it has an excess charge), and you have already calculated the electric field from part a). Plugging in these values, you can calculate the force.
c) To find the number of excess electrons on the oil drop, recall that the charge of an electron is -1.6 × 10^-19 C. You can divide the total charge on the oil drop (-1.31 × 10^-17 C) by the charge of a single electron to find the number of excess electrons.
d) To calculate the kinetic energy of the oil drop when it arrives just below the upper plate, you can use the equation:
Kinetic energy (KE) = 1/2 × Mass (m) × Velocity^2
Since the problem statement mentions that you can ignore non-electrical effects like gravity, we know that the electric field between the plates will accelerate the oil drop. The oil drop will gain kinetic energy as it moves from the lower plate to the upper plate. To find the velocity, you can use the formula:
Velocity (v) = Acceleration (a) × Time (t)
The acceleration can be found using Newton's second law, where Force (F) is the electrical force from part b) and Mass (m) is given as 4.00 × 10^-6 kg. After you find the acceleration, you can calculate the time it takes for the oil drop to reach the upper plate using the equation:
Time (t) = Distance (d) / Velocity (v)
Finally, you can plug in the values of mass, velocity, and time into the equation for kinetic energy to calculate the answer.
I hope this explanation helps you understand how to approach and solve these questions!