How do you calculate the electric field due to a uniform charge distribution?

To calculate the electric field due to a uniform charge distribution, use Coulomb's law and integration.

Coulomb's law states that the electric field at a point due to a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the point charge. For a uniform charge distribution, we can break up the distribution into infinitesimal charge elements and use integration to find the total electric field at a point.

Let's consider a uniform charge distribution along the x-axis. We can break up the distribution into small charge elements, dq, and find the electric field due to each element using Coulomb's law. The electric field due to a small charge element at a distance r from the point is given by dE = k(dq/r^2), where k is the Coulomb constant.

To find the total electric field at a point, we need to integrate the electric field due to all the charge elements. For a one-dimensional uniform charge distribution, the integration becomes a simple integral. The total electric field at a point due to a uniform charge distribution is given by E = kq/r^2, where q is the total charge and r is the distance from the point to the centre of the distribution.

In summary, to calculate the electric field due to a uniform charge distribution, break up the distribution into small charge elements, find the electric field due to each element using Coulomb's law, and integrate to find the total electric field at a point.