To solve this problem, we need to analyze the circuit with the ideal diode.$\\$Given:$\\$• Voltage at point A is $+4 \,$V.$\\$• Voltage at point B is $-6 \,$V.$\\$• Resistor value is $1 \,$k$\Omega. \\$Step 1: Determine the direction of current flow.$\\$• The diode allows current to flow from higher to lower potential.$\\$• Voltage at A is higher than at B, so the diode is forward-biased.$\\$Step 2: Calculate the voltage across the resistor.$\\$• Voltage across AB is $(4 - (-6)) \,$V$= 10 \,$V.$\\$Step 3: Use Ohm's Law to find the current.$\\ I = \frac{V}{R} \\ I = \frac{10 \, V}{1 \, k\Omega} \\ I = \frac{10}{1000} \, A \\ I = 0.01 \,$A$\\$Therefore, the current flowing through AB is $0.01 \,$A$,$ which is $10^{-2} \,$A.$\\$This corresponds to Option 4.