A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter. The current density in the proton beam increases linearly with distance from the center. This is expressed mathematically as J(r) = J0 (r/R), where R is the radius of the beam and J0 is the current density at the edge. Determine the value of J0. A) 25 A/m² B) 6.2 A/m² C) 12 A/m² D) 17 A/m²

Question

Quizplus · Accepted Answer

The current density at the edge of the beam (r = R) can be determined by substituting r = R and J(r) = J0 into the given equation:

J(R) = J0 (R/R) = J0

Therefore, J0 = J(R) = 1.3 mA / [(π/4)(10.0 mm)^2] = 26.2 A/m²

Rounding to one significant figure, the answer is 25 A/m², which corresponds to choice A.

A Proton Beam That Carries a Total Current of 1