Question

hw23 electric fields and equipotential surfaces. the dashed lines in the diagram represent cross - sections of equipotential surfaces drawn in 1 v increments. (figure 1) part a what is the work done by the electric force to move a 1 c charge from a to b? express your answer in joules. view available hint(s) part b what is the work done by the electric force to move a 1 c charge from a to d? express your answer in joules. view available hint(s)

Explanation:

Step1: Recall work - potential formula

The work done \(W\) by the electric force in moving a charge \(q\) between two points with potential difference \(\Delta V\) is given by \(W = q\Delta V\).

Step2: Determine potential difference for Part A

For moving from point \(A\) to \(B\), the potential at \(A\) is \(V_A=- 1V\) and at \(B\) is \(V_B = 0V\). So, \(\Delta V_{AB}=V_B - V_A=0 - (-1)=1V\), and \(q = 1C\). Then \(W_{AB}=q\Delta V_{AB}=1C\times1V = 1J\).

Step3: Determine potential difference for Part B

For moving from point \(A\) to \(D\), the potential at \(A\) is \(V_A=-1V\) and at \(D\) is \(V_D=-2V\). So, \(\Delta V_{AD}=V_D - V_A=-2V-(-1V)= - 1V\), and \(q = 1C\). Then \(W_{AD}=q\Delta V_{AD}=1C\times(-1V)=-1J\).

Answer:

Part A: 1 J
Part B: - 1 J