Question

An electrical charge of $2$ $\mu$C is placed at the point $(1,2,3)$. At the point $(2,3,4)$ the electric field and potential will be :

• A. $6\times {10}^{3}N{C}^{-1}$ and $6\times {10}^{3}J{C}^{-1}$
• B. $6000N{C}^{-1}$ and $6000\sqrt{3}J{C}^{-1}$
• C. $6\times {10}^{3}N{C}^{-1}$ and $3\sqrt{3}J{C}^{-1}$
• D. none of the above

Answer 1

The correct option is B $6000N{C}^{-1}$ and $6000\sqrt{3}J{C}^{-1}$

The electric field , $E=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}=9\times {10}^9\times \frac{2\times {10}^{-6}}{(2-1{)}^2+(3-2{)}^2+(4-3{)}^2}=6000N{C}^{-1}$

and potential, $V=\frac{1}{4\pi {ϵ}_0}\frac{q}{r}=9\times {10}^9\times \frac{2\times {10}^{-6}}{\sqrt{(2-1{)}^2+(3-2{)}^2+(4-3{)}^2}}=6000\sqrt{3}N{C}^{-1}$