A junction is just a point of wire; it has no room to store charge. So in the steady state the current arriving must exactly equal the current leaving. That single statement of charge conservation is Kirchhoff's first law: the signed sum of currents at any node is zero.
Two wires carry currents Iā and Iā towards a junction. The beads are charge, and their speed is the current.
Junction rule I₃ = I₁ + I₂ = ā A
net current at the node ΣI = I₁ + I₂ − I₃ =
ā A (zero, always)