Question

# The electric potential $$V$$ at any point $$\left( x,y,z \right)$$ in space is given by $$V=3{ x }^{ 2 }$$ where $$x, y, z$$ are all in metre. The electric field at the point $$\left( 1m,0,2m \right)$$ is

A
6Vm1 along negative x-axis
B
6Vm1 along positive x-axis
C
12Vm1 along negative x-axis
D
12Vm1 along positive x-axis
E
8Vm1 along negative x-axis

Solution

## The correct option is A $$6V{ m }^{ -1 }$$ along negative $$x$$-axisElectric potential $$V=3{ x }^{ 2 }$$$$E=-\dfrac { dV }{ dx }$$$$E=-\dfrac { d }{ dx } \left( 3{ x }^{ 3 } \right)$$$$E=-6x$$At the point $$\left( 1,0,2 \right)$$Electric field $$E=6\times 1=-6{ V }/{ m }$$Thus electric field at $$(1m,0,2m)$$ is  $$6Vm^{-1}$$ along negative $$x-$$ axis.PhysicsNCERTStandard XII

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