Question

The potential in a certain region of space is given by the function $x{y}^2{z}^3$ with respect to some reference point. Find the y-component of the electric field at $(1,-3,2)$.

• A. $48\hat{j}$
• B. $48\hat{i}$
• C. $-48\hat{i}$
• D. $-48\hat{j}$

Answer 1

The correct option is A $48\hat{j}$

given potential $=x{y}^2{z}^2$

we have to find the y-component of electric field at $(1,-3,2)$

here, we use the relation b/w electric field and the potential $E=\frac{-dv}{dr}$

To find y- c ordinate of electric field, we differential function of V and y.

so,$E_y=\frac{-dv}{dy}=\frac{-d}{dy}\left(x{y}^2{z}^3\right)$

$E_y=-2xy{z}^3$

To find electric field at pt. $(1,-3,2)$

we substitute for $x=1$

$y=-3$

$z=2$

we get$E_y=-2\left(1\right)(-3){\left(2\right)}^3$

$=48$

Hence the answer is $48\hat{j}$

so, the correct answer is option $\left(a\right).$