Potential Difference and Work

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Electrostatics Intermediate Electric Potential

Source: High school physics (Chinese)

Problem Sets:

Electrostatics

Problem

The potential difference $U_{AB}$ between points A and B in an electric field is -150 V. A test charge of $q = -3 \times 10^{-6}$ C is moved from point B to point A.

  1. Which point, A or B, has a higher potential?
  2. How much work is done by the electric field?

[Q1] Point B [Q2] $W_{BA} = -4.5 \times 10^{-4}$ J

[Q1] The potential difference $U_{AB}$ is defined as $U_{AB} = U_A - U_B$. Given $U_A - U_B = -150$ V, it follows that $U_A < U_B$. Therefore, point B has a higher potential.

[Q2] The work $W_{BA}$ done by the electric field in moving the charge from B to A is:

$$W_{BA} = q(U_B - U_A) = q U_{BA}$$

We know that $U_{BA} = U_B - U_A = -(U_A - U_B) = -U_{AB} = -(-150 \text{ V}) = 150 \text{ V}$.

$$W_{BA} = (-3 \times 10^{-6} \text{ C})(150 \text{ V})$$ $$W_{BA} = -4.5 \times 10^{-4} \text{ J}$$