The current density of the proton beam at the edge is 8.275 A/m².
The given parameters;
The radius of the beam is calculated as follows;
[tex]R = \frac{d}{2} \\\\R = \frac{10 \ mm}{2} \\\\R = 5 \ mm[/tex] = 5 x 10⁻³ m
Current density is calculated as follows;
[tex]J = \frac{I}{A} \\\\[/tex]
where;
A is the area of the beam
Area of the beam is calculated as follows;
A = πr²
A = π x (5 x 10⁻³)²
A = 7.855 x 10⁻⁵ m²
The current density is calculated as follows;
[tex]J = \frac{I}{A} \\\\J = \frac{1.3 \times 10^{-3} }{7.855\times 10^{-5}} \\\\J = 16.55 \ A/m^2[/tex]
Since the current density increases with distance;
[tex]J_0 = J \times \frac{R}{r} \\\\J_0 = 16.55 \times \frac{5 \times 10^{-3} }{10 \times 10^{-3}} \\\\J_0 = 8.275 \ A/m^2[/tex]
Thus, the current density of the proton beam at the edge is 8.275 A/m².
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