4 packets of charges are arranged in a circle. Each packet is 90 degrees from each other. Each packet consists of 22 elementary charges associated with the nucleus of two sodium atoms. A test charge is placed in the center of the circle of packets. The distance between the test charge and any packet is 10m. What is the net force on the test charge?
Looking on how to solve this. Not just an answer
hey, if you put a negative 1 charge at (0,0)
a + 1 charge at (1,0)
and +1 charge at -1, 0
The middle one will be pulled left exactly as much as right!
The net effect is zero.
Alright thanks. I knew that but the question seemed to ask for much more. I guess it was just filler information to throw me off.
They did not tell you if the test charge was one +1e or -1 e or +1 Coulomb or -1 Coulomb or whatever so it was impossible to do numbers anyway.
To solve this problem, let's break it down step by step:
Step 1: Calculate the total charge in each packet.
Each packet consists of 22 elementary charges associated with the nucleus of two sodium atoms. The elementary charge is the charge of a single proton or electron, which is approximately 1.6 x 10^-19 coulombs. So, the total charge in each packet is:
Total charge = 22 x elementary charge
Total charge = 22 x 1.6 x 10^-19 C
Step 2: Calculate the electric field due to each packet at the center.
The electric field due to a point charge can be calculated using Coulomb's law:
Electric field (E) = (k x Q) / r^2
Where:
- k is the electrostatic constant, approximately 9 x 10^9 N m^2/C^2
- Q is the total charge of the packet
- r is the distance between the center and the packet, which is 10 meters in this case
Step 3: Calculate the net electric field at the center.
Since the packets are arranged in a circle, each packet contributes to the net electric field at the center. As the packets are 90 degrees from each other, we can use vector addition to find the net electric field.
Net electric field = Σ(E_i)
Where Σ denotes the summation, and E_i represents the electric field due to each packet.
Step 4: Calculate the net force on the test charge.
To find the net force on the test charge, we need to multiply the net electric field by the charge of the test charge. Let's assume the test charge is positive, for simplicity.
Net force = q x E_net
Where:
- q is the charge of the test charge
- E_net is the net electric field at the center
By following these steps, you should be able to find the answer to the problem.