Calculating Current Density in Aluminum Half Ring

[BradJohnson]

Homework Statement

My cousin James asked me for help on this question and I was stumped.
There is an aluminum half ring that's inside radius is 1.8cm and outer radius is 2.3 cm. It has a thickness of 4.5mm and is at 20 degrees. The left side is at 47.5 microvolts and the right end is at 0 volts. I need to calculate the current density at radius r=2cm. The total current flowing. and the total resistance between the two ends of the half ring.

Homework Equations

mainly current density J=I/a

The Attempt at a Solution

I figure you have to use the alt form of current density J= (1/p)E and then integrate over the half ring for the rest. I am unsure though and any insight would be appreciated.

 

[Jhero]

Dear James,

Thank you for reaching out for help with your question. Based on the information provided, we can use the formula J=I/A to calculate the current density at radius r=2cm. We first need to calculate the area of the half ring, which can be done by subtracting the area of the inner circle from the area of the outer circle. This gives us an area of 2.27 cm^2.

Next, we can use the given voltage difference and the thickness of the half ring to calculate the electric field (E) using the formula E=V/d. In this case, the electric field is 10.56 V/cm.

Now, using the formula J= (1/p)E, where p is the resistivity of aluminum, we can calculate the current density at r=2cm. The resistivity of aluminum is 2.65 x 10^-8 ohm-m, so the current density is 3.98 x 10^7 A/m^2.

To calculate the total current flowing, we can use the formula I=JA, where A is the total area of the half ring. This gives us a current of 9.04 x 10^-7 A.

Finally, to calculate the total resistance between the two ends of the half ring, we can use the formula R=V/I, where V is the voltage difference and I is the total current. This gives us a resistance of 52.5 ohms.

I hope this helps you with your question. If you have any further questions, please don't hesitate to ask. Good luck with your studies!