Electrostatics Question 442
Question: Electric potential at any point is $ V=-5x+3y+\sqrt{15}z $ , then the magnitude of the electric field is [MP PET 2002]
Options:
A) $ 3\sqrt{2} $
B) $ 4\sqrt{2} $
C) $ 5\sqrt{2} $
D) 7
Show Answer
Answer:
Correct Answer: D
Solution:
$ E _{x}=-\frac{dV}{dx}=-(-5)=5; $
$ E _{y}=-\frac{dV}{dy}=-3 $ and $ E _{z}=-\frac{dV}{dz}=-\sqrt{15} $
$ E _{net}=\sqrt{E _{x}^{2}+E _{y}^{2}+E _{z}^{2}}=\sqrt{{{(5)}^{2}}+{{(-3)}^{2}}+{{(-\sqrt{15})}^{2}}}=7 $
