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- Homework Statement
- Strugling to get the E from its V at the centre of the semicircle.

- Relevant Equations
- V = k*lambda* pi

pi = 3.1415

lambda = charge density

k = 1 / (4*pi*eo)

According to theory I should be able to get the Electric Field (E) from its pOtential (V) by doing the grad (V) so

E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing??

see figure below

The answer should be Ex = 2*k*lambda / r

This is how I calculate V:

dV = k * dQ/r = k*r*d(theta)*lambda / r

dV = k*lambda * d(theta)

Integrating from 0 to pi

V = k* lambda * pi.

E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing??

see figure below

The answer should be Ex = 2*k*lambda / r

This is how I calculate V:

dV = k * dQ/r = k*r*d(theta)*lambda / r

dV = k*lambda * d(theta)

Integrating from 0 to pi

V = k* lambda * pi.

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