This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values. The potential difference of the battery is V_battery = 12 \, V. The charge of an electron is q = -1.602 × 10^-19 \, C. Step 2: Determine the change in potential. The electron is carried from the positive terminal to the negative terminal. The positive terminal is at a higher potential than the negative terminal. Let V_+ be the potential of the positive terminal and V_- be the potential of the negative terminal. We know that V_+ - V_- = 12 \, V. The initial potential is V_initial = V_+. The final potential is V_final = V_-. The change in potential experienced by the electron is V = V_final - V_initial = V_- - V_+. Therefore, V = -12 \, V. Step 3: Calculate the work required. The work W required to move a charge q through a potential difference V is given by the formula: W = q V Substitute the values: W = (-1.602 × 10^-19 \, C) × (-12 \, V) W = 1.9224 × 10^-18 \, J Rounding to two significant figures, consistent with the given voltage: W = 1.9 × 10^-18 \, J The work required is positive because an electron (negative charge) is being moved from a higher potential (positive terminal) to a lower potential (negative terminal), which is against the direction it would naturally move under the influence of the electric field. The work required is 1.9 × 10^-18 \, J. That's 2 down. 3 left today — send the next one.