Looking for classes? Ksquare Career Institute, Bengaluru →
If potential (in volts) in a region is expressed as $V(x,y,z) = 6xy - y + 2yz$, the electric field (in N/C) at point (1, 1, 0) is:
A
$-(6\hat i + 9\hat j + \hat k)$
B
$-(3\hat i + 5\hat j + 3\hat k)$
C
$-(6\hat i + 5\hat j + 2\hat k)$
D
$-(2\hat i + 3\hat j + \hat k)$
Detailed Solution
$\vec E = -\left(\frac{\partial V}{\partial x}\hat i + \frac{\partial V}{\partial y}\hat j + \frac{\partial V}{\partial z}\hat k\right)$
$\vec E = -(6y)\hat i - (6x - 1 + 2z)\hat j - (2y)\hat k$
At (1, 1, 0): $\vec E = -(6\hat i + 5\hat j + 2\hat k)$
$\vec E = -(6y)\hat i - (6x - 1 + 2z)\hat j - (2y)\hat k$
At (1, 1, 0): $\vec E = -(6\hat i + 5\hat j + 2\hat k)$