- #1

sergioro

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## Homework Statement

A question involving the relationship between the electric

field

**E**(

**r**) and the electric potential V(

**r**) is about computing the electric

field on the z-axis due to a uniform line charge distribution λ

spread out on a semicircle of radius R, lying on the first

half of the XY plane (0 ≤ θ ≤ π). A few points on the

semicircle are (x=R,y=0) at θ= 0, (x=0,y=R) at θ= π/2,

and (x=-R,y=0) at θ = π (I am using the symbol π as Pi).

## Homework Equations

The electric potential V(

**r**) is easily computed giving the result

V(z) = K*Q/Sqrt(z^2 + R^2). Q = λπR and K is the electric constant.

## The Attempt at a Solution

The electric field is suppose to be

obtained via E = - grad(V) = - d(V(z))/dz. But this relation leads only

to one component of the electric field.

Could somebody point out what is missing?

Sergio