Solutions To The Spherical Wave Equation

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When t=0 and r approaches zero in the spherical wave equation E(r, t) = (A/r)exp{i(k.r-ωt)}, the expression becomes problematic due to division by zero. Taking the limit as r approaches zero while keeping t at zero leads to the exponential term approaching 1, resulting in the expression A/r, which is still undefined. This indicates a singularity at the origin, highlighting the limitations of the model in this scenario. The discussion emphasizes the need for careful consideration of limits in wave equations. Understanding these mathematical nuances is crucial for solving spherical wave equations effectively.
RESolo
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If the solution to the electric part of the spherical wave equations is:

E(r, t) = ( A/r)exp{i(k.r-ωt)

What happens when t=0 and the waves originates at the origin, i.e. r=0 ... which I assume can't be right as you of course cannot divide by zero.

Thanks!
 
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Hint: what happens if you take the limit towards zero of r and take t=0?
 
Te exponential approaches 1 and you have A/r, the same problem? Can you just tell me I'm running out of time here!
 
RESolo said:
Can you just tell me I'm running out of time here!

I can't PF rules won't let me.
 

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