A 68.0 g hollow copper cylinder is 90.0 cm long and has an inner diameter of 1.0 cm. The current density along the length of the cylinder is 1.60×10^5(A/m^2). What is the current in the cylinder? Ive tried many ways but am not getting the correct answer.
You have to measure the area of the cylinder, that is, the outer radius area minus the inner radius.
You are given the mass, you can look up the density.
mass=density*PI(radiusouter^2-radiusinner^2)*length
Now, solve for (radiusouter^2-radiuinner^2)
Areacopper= PI (radiusouter^2-radiusinner^2) or
areacopper= masscopper/(density*lenght)
current= currentdensity*area
So, did the size of the cylinder affect anything?
There is no inner or outer im guessing it is assumed to be negligibly thick
Nvm Thank you for the insight into the density. I got the anwser now and your right the radius has nothing to do with it.
To find the current in the cylinder, we can use the formula:
I = J * A
where I is the current, J is the current density, and A is the cross-sectional area of the cylinder.
To calculate the cross-sectional area, we need to subtract the area of the inner circle from the area of the outer circle.
The area of a circle can be calculated using the formula:
A = π * r^2
where A is the area and r is the radius of the circle.
Given that the inner diameter of the cylinder is 1.0 cm, the radius of the inner circle will be 0.5 cm.
Let's calculate the radius of the outer circle. The inner diameter is 1.0 cm, so the outer diameter will be 1.0 cm + 2 * (0.5 cm) = 2.0 cm. Therefore, the radius of the outer circle will be 1.0 cm.
Now, we can calculate the cross-sectional area of the cylinder:
A = π * (r_outer^2 - r_inner^2)
A = π * (1.0 cm^2 - 0.5 cm^2)
A = π * (1.0 cm^2 - 0.25 cm^2)
A = 0.75 π cm^2
Next, we can calculate the current using the current density and the cross-sectional area:
I = J * A
I = (1.60×10^5 A/m^2) * (0.75 π cm^2)
When working with dimensions, it is important to ensure that the units are consistent. In this case, we need to convert the units of the current density from A/m^2 to A/cm^2. Since 1 m = 100 cm, the conversion factor is 1 m^2 = (100 cm)^2 = 10,000 cm^2. Therefore, we can multiply the current density by 10,000 to convert the units:
I = (1.60×10^5 A/m^2) * (10,000 cm^2)
I = 1.60×10^9 A/cm^2
Now, we can calculate the current:
I = 1.60×10^9 A/cm^2 * 0.75 π cm^2
I = 3.60×10^9 π A
I ≈ 1.13×10^10 A
Therefore, the current in the cylinder is approximately 1.13×10^10 A.