Show that the electric field at the surface of a charged conductor is given by `vecE = (sigma)/(epsi_(0)) hatn` , where `sigma` is the surface charge density and `hatn` is a unit vector normal to the surface in the outward direction .

Explanation

To show that the electric field at the surface of a charged conductor is given by \( \vec{E} = \frac{\sigma}{\epsilon_0} \hat{n} \), where \( \sigma \) is the surface charge density and \( \hat{n} \) is a unit vector normal to the surface in the outward direction, we can proceed as follows:

### Step-by-Step Solution:

1. **Consider a small patch of the surface of the conductor:**
- Let the surface charge density be \( \sigma \) (charge per unit area).
- The total charge on a small area \( dA \) of the surface is \( dq = \sigma dA \).

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