Question
Read each statement below carefully and state, with reasons and examples, if it is true or false:
A scalar quantity is one that
Does not vary from one point to another in space.
A scalar quantity is one that
Does not vary from one point to another in space.
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$\text{U}(\overrightarrow{\text{r}_2})-\text{U}(\overrightarrow{\text{r}_1})=-\int\limits^{\vec{\text{r}}_2}_{\vec{\text{r}_1}} \vec{\text{B}}.\text{d}\vec{\text{l}}.$
Apply this equation to a closed curve enclosing a long atraicht wire. The RHS of the above equation is then
$-{\mu}_\text{o} \text{ i}$ by Ampere's law. We see that $\text{U}(\vec{\text{r}_2})\neq\text{U}(\vec{\text{r}_1})$ even when $\vec{\text{r}_2}=\vec{\text{r}_1}.$Can we have a magnetic acalar potential in this case?