# Solving Retarded Potentials Homework: Electric & Magnetic Fields

• stunner5000pt
The only thing you need to be careful about is the limits of integration. The upper limit should be z = sqrt(c^2t^2 - s^2), not sqrt(c^2t^2 - s^2). Other than that, your logic seems sound and I don't see any errors.
stunner5000pt

## Homework Statement

Suppose a wire carries a current such taht
I(t) = 0 for t< = 0
= k t for t > 0
Find the electric and magnetic fields generated

2. The attempt at a solution
trying to figure out vector potential first
looking at the diagram
s is the distance fro a point P to the wire which is positioned on the Z axis.
r' is the distance to some section of the wire dz

the only contribution is for t > s/c, otherwise the em fields haven't reached the point P

we only need to integrate along the z since there is X and Y symmetry

$$z = \pm \sqrt{c^2 t^2 - s^2}$$
but we are going to get the EM fields from time $= t - r' / c = t - \frac{\sqrt{z^2 + s^2}}{c}$

so we're lookign at integrating this

$$A = \frac{\mu_{0}}{4 \pi} 2 \int_{0}^{\sqrt{c^2 t^2 - s^2}} \frac{k (t-\frac{\sqrt{z^2 + s^2}}{c}}{\sqrt{z^2 + s^2}} dz$$

ahve i gone wrong somewhere??

something wrong in my logic?

thanks for any and all input!

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stunner5000pt said:
$$A = \frac{\mu_{0}}{4 \pi} 2 \int_{0}^{\sqrt{c^2 t^2 - s^2}} \frac{k (t-\frac{\sqrt{z^2 + s^2}}{c}}{\sqrt{z^2 + s^2}} dz$$

That looks correct to me

## What are retarded potentials in the context of electric and magnetic fields?

Retarded potentials are mathematical functions used to describe the behavior of electric and magnetic fields in the past. They take into account the finite speed of electromagnetic waves and how they interact with charges and currents in a given system.

## Why is solving retarded potentials important in studying electric and magnetic fields?

Solving retarded potentials allows us to accurately predict the behavior of electric and magnetic fields in a given system. It also helps us understand how these fields interact with charges and currents in the past, which is crucial in many applications such as communication technology and astrophysics.

## What are the key equations used in solving retarded potentials?

The key equations used in solving retarded potentials are the electric field equation, the magnetic field equation, and the wave equation. These equations can be solved using various techniques such as Green's functions and boundary value problems.

## What are some common challenges in solving retarded potentials?

One common challenge in solving retarded potentials is the complexity of the equations involved, which can be difficult to solve analytically. Another challenge is accurately modeling the system and accounting for all relevant factors, such as boundary conditions and non-linearities.

## How can one improve their understanding of solving retarded potentials?

Improving understanding of solving retarded potentials can be achieved through studying the underlying mathematical concepts, practicing with various problems and applications, and seeking guidance from experienced professionals or educational resources. It is also important to have a strong foundation in electromagnetism and mathematical techniques such as vector calculus and differential equations.

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