Points A [at (3,6)m] and B [at (8,-3)m] are in a region where the electric field is uniform and given by $\overrightarrow { \mathrm { E } } = 12{ \tilde { i } }$ N/C.What is the electric potential difference V_A - V_B? A)+60 V B)-60 V C)+80 V D)-80 V E)+50 V

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Quizplus · Accepted Answer

The electric potential difference between two points is given by:$$V_A - V_B = -\int_A^B \overrightarrow { \mathrm { E } } \cdot d\overrightarrow { \mathrm { l } }$$In this case, the electric field is uniform, so we can take it outside the integral:$$V_A - V_B = -\overrightarrow { \mathrm { E } } \cdot \int_A^B d\overrightarrow { \mathrm { l } }$$The integral of $d\overrightarrow { \mathrm { l } }$ is simply the displacement vector from point A to point B:$$\overrightarrow { \mathrm { l } } = \overrightarrow { \mathrm { r } }_B - \overrightarrow { \mathrm { r } }_A = (8,103) - (3,6) = (5,97)$$So, the electric potential difference is:$$V_A - V_B = -(12\hat{i}) \cdot (5\hat{i} + 97\hat{j}) = -60 V$$Therefore, the correct answer is A.

Points a [At (3,6)m] and B [At (8,-3)m] Are in a Region