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Electric Potential and Potential Difference

The electric ...

Question

The electric potential decreases uniformly from 100 V to 50 V as one moves along the x-axis from x =0 to x =5 m. The electric field at x = 2 m is equal to 10 V/m. Is this statement true or false.

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Solution

Electric field is given by $E = - \frac{d V}{d r}$ and here $r = x$ only
So, $E = - \frac{d V}{d r} = - \frac{50 - 100}{5 - 0} = - (- 10) = 10 V / m$
It is given that electric potential decreases uniformly this means electric field is uniform. Therefore, statement is true.

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