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- A wire of 60\,cm length and mass 10\,gm is suspended by a pair of flexible leads in a magnetic field of 0.40\,weber/m$^2$. What are the magnitude and the direction of the current required to remove the tension in the supporting leads? (See Fig 1.) \hfill[8]
- What is vector potential? How is the magnetic field related to the vector potential and what is the basis of this relation?
- Let $$\vec{A}(\vec{r}) = \lambda \hat{n}\times \vec{r}$$ where $\lambda$ and $\hat{n}$ independent of $\vec{r}$. Show that this vector potential corresponds to a uniform magnetic field $\vec{B}=B_0 \hat{n}$ and relate $\lambda$ to $B_0$. \hfill[6]
- Two long wires held parallel to the $z$- axis and carrying current $I$ in opposite directions cross the $X$-$Y$ plane at $(-a,0)$ and $(a,0)$. Derive an expression for magnetic field as function of $x$. Skech a graph to show the variation of the magnetic field as function of $x$. Take the magnetic field positive if it points along positive $y$ axis and negitive if it points along negative $y$ axis.
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