A region contains a uniform electric field $\mathbf{E}=(10 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}) \mathrm{Vm}^{-1} . A$ and $B$ are two points in the field at $(1,2,0) \mathrm{m}$ and $(2,1,3) \mathrm{m}$, respectively. The work done when a charge of $0.8 \mathrm{C}$ moves from $A$ to $B$ in a…

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A region contains a uniform electric field $\mathbf{E}=(10 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}) \mathrm{Vm}^{-1} . A$ and $B$ are two points in the field at $(1,2,0) \mathrm{m}$ and $(2,1,3) \mathrm{m}$, respectively. The work done when a charge of $0.8 \mathrm{C}$ moves from $A$ to $B$ in a parabolic path is

Aicharya · Accepted Answer

Using $\mathrm{E}=\frac{d V}{d r}$ or, $\mathrm{dV}=\mathrm{E} \mathrm{dr}$ Displacement, $\mathrm{dr}=\mathrm{r}_{\mathrm{B}}-\mathrm{r}_{\mathrm{A}}$ $\begin{aligned} & =(2 \hat{i}+\hat{j}+3 \hat{k})-(\hat{i}+2 \hat{j}) \ & =(10 \hat{i}+30 \hat{j})(\hat{i}-\hat{j}+3 \hat{k}) \ & =10 \hat{i} \cdot \hat{i}-30 \hat{i} \cdot \hat{j}+0 \ & =10-30=-20 \end{aligned}$ Work done, $\mathrm{W}=\mathrm{q} 	imes|\mathrm{dV}|=0.8(20)=16 \mathrm{~J}$

A region contains a uniform electric field $\mathbf{E}=(10 \hat{\mathbf{i}}+30 \hat{\mathbf{j}})…

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