Hello, this is Bing. I can help you with this question.
The total charge of the system is obtained by integrating the linear charge density over the length of the system. Assuming the system is a line segment from x = 0 to x = L, we have:
$Q = \int_0^L \lambda(x) dx = \int_0^L (x+1)\delta(2x) dx$
Using the property of the Dirac delta function, we can simplify the integral as:
$Q = \frac{1}{2}(0+1)\delta(0) = \frac{1}{2}$
Therefore, the total charge of the system is **0.5 C**.
If you want to learn more about linear charge density and its applications, you can check out these links:
- [Charge density - Wikipedia](^1^)
- [Explain linear charge density. Write it's unit. - Toppr](^2^)
- [Linear, Surface Charge and Volume Charge Density - Vedantu](^3^)
- [Formula of Linear charge density & its calculation - Edumir-Physics](^4^)
I hope this helps. Have a nice day!
Source: Conversation with Bing, 04/01/2024
(1) Charge density - Wikipedia. https://en.wikipedia.org/wiki/Charge_density.
(2) Explain linear charge density. Write it's unit. - Toppr. https://www.toppr.com/ask/question/explain-linear-charge-density-write-its-unit/.
(3) Linear, Surface Charge and Volume Charge Density - Vedantu. https://www.vedantu.com/physics/charge-density-formula.
(4) Formula of Linear charge density & its calculation - Edumir-Physics. https://electronicsphysics.com/linear-charge-density-formula/.
