Question

electric fields and equipotential surfaces
the dashed lines in the diagram represent cross sections of equipotential surfaces drawn in 1 v increments. (figure 1)
figure
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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.
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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.

Explanation:

Step1: Recall work - potential difference formula

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

Step2: Calculate potential difference for part A

The potential at point $A$ is $0\ V$ and at point $B$ is $1\ V$. So, $\Delta V_{AB}=V_B - V_A=1 - 0=1\ V$. Given $q = 1\ C$, then $W_{AB}=q\Delta V_{AB}=1\times1 = 1\ J$.

Step3: Calculate potential difference for part B

The potential at point $A$ is $0\ V$ and at point $D$ is $- 3\ V$. So, $\Delta V_{AD}=V_D - V_A=-3 - 0=-3\ V$. Given $q = 1\ C$, then $W_{AD}=q\Delta V_{AD}=1\times(-3)=- 3\ J$.

Answer:

Part A: 1 J
Part B: -3 J