 # Retarded Potential Questions

## Question

Retarded Potential of a point charge
i)Use a spreadsheet software to graph the potential V(r,t)-vs-t (use range between -500nsto +500ns) at a point 1 meters along the y-axis, due to a point charge moving with constant relativistic speed β=v/c along the x-axis. Assume the charge is at the origin attˈ= 0 (t’ retarded time). Plot for values of β equal to 0.1; 0.5; 0.9; 0.99, on the same graph (Graph1).
For each value of β show t vs tˈ on the same graph (Graph2).
Normalise values to the potential due to the static charge at the origin.
ii)Derive (analytically) expressions for retarded position [x], for tˈ and t when the potential is at its maximum value.

## Solution Preview

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%potential variation with time
clear
t=(-500:0.1:500);
k=1;%q/4pie=1
b=0.1;
c=3*10^8;
p=k./sqrt(1+b^2*(c^2*t.^2*(10^-18)-1));
figure
plot(t,p,'r')
grid on
hold on
b=0.5...
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