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Figures \((a)\) and \((b)\) show the field lines of a positive and negative point charge respectively.
Question: Figures (a) and (b) show the field lines of a positive and negative point charge respectively.Give the signs of the potential difference  V_{text P}-V_{text Q} and V_{text B}-V_{text A} .
Give the signs of the potential difference  \(V_{\text P}-V_{\text Q}\) and \(V_{\text B}-V_{\text A} .\)

Answer

\(\left. \left({V}_{P}−{V}_{Q}\right)\right.\)- Positive. \(\left(V_B-V_A\right)\)-Negative
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Solution

Solution -
As potential is given by\(V\;=\;\dfrac{1}{4\pi {\varepsilon }_{0}}\dfrac{q}{r}\)
or  \(V\;\propto \;\frac{1}{r}\)
So, \({V}_{P}\;> \;{V}_{Q}\).
Thus,  \(\left. \left({V}_{P}−{V}_{Q}\right)\right.\)  is positive.
Also \(V_B\)  is less negative than  \(V_A\)in fig (b)
Thus,  \({V}_{B}\;> \;{V}_{A}\)
But in this case the charge is negative
so  \(\left(V_B-V_A\right)\)  is negative
Hence, \(\left. \left({V}_{P}−{V}_{Q}\right)\right.\)  is positive and \(\left(V_B-V_A\right)\)  is negative.
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