# Total Charge of a Circular Wire

A circular wire of radius $$a$$ has linear charge density $$\lambda=\lambda_0cos^2\theta$$ where $$\theta$$ is the angle with respect to a fixed radius. Calculate the total charge.

Solution:

Charge on an element $$dl=ad\theta$$ is $$\lambda_0cos^2\theta.ad\theta$$
Total charge $$Q=\int_{0}^{2\pi}a\lambda_0cos^2\theta d\theta$$$$=a\lambda_0\pi$$