Question

# The potential at a point x (measured in m) due to some charges situated on the x-axis is given by  V(x) = (20 /x$$^{2}$$- 4) volts. The electric field E at $$x = 4 m$$ is given by :

A
5/3 Volt/m and in the ve x direction
B
5/3Volt/m and in the +ve x direction
C
10/9 Volt/m and in the ve x direction
D
10/9 Volt/m and in the +ve x direction

Solution

## The correct option is A $$10/9$$ Volt/m and in the $$+ve$$ x directionThe relation between Electric field and electrostatic potential is given by $$\displaystyle \vec{E} = -\nabla V$$In one dimension, $$\vec{E} = \displaystyle -\frac{dV}{dx}$$Given $$V = \displaystyle \frac{20}{x^2-4}$$Thus, $$E = -\displaystyle \frac{dV}{dx} = \frac{40x}{(x^2-4)^2}$$Thus Field at $$x = 4\textrm{ m}$$ is given by $$E = \displaystyle\frac{40\times 4}{(4^2-4)^2} = +\frac{10}{9} \textrm{ V/m}$$The field is in the positive $$x$$ directionPhysicsNCERTStandard XII

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