Determine the amount of charge passing through the cross-section of the conductor during 10

Determine the amount of charge passing through the cross-section of the conductor during 10 s, if the current in the conductor during this time increases uniformly from 0 to 100A.

Task data: Δt (duration of the passage of the charge) = 10 s; I1 (initial amperage) = 0 A; I (final amperage) = 100 A.

1) The current strength at a given time t: I = I0 + k * t, whence for our conditions k = (I – I0) / t = (100 – 0) / 10 = 10 and I = 10t.

2) Amount of charge: q = 010∫ Idt = 010∫ 10tdt = 10t ^ 2/2 = 10 * 10 ^ 2/2 = 500 C.

Answer: A charge of 500 C managed to pass through the cross-section of the conductor.