First slide

Electrostatic potential

Question

The electric potential in a region along the X-axis varies with x according to the relation V (x) = 4 + 5 x² Then

Moderate

A

potential difference between the points x = 1 and x = -2 is 15 volt
B

forced experienced by one coulomb charge at x= - 1 m will be 10 N
C

the force experienced by the above charge will be towards + X-axis
D

a uniform electric field exists in this region along the x-axis

Solution

Given that $\dot{V} (x) = 4 + 5 x^{2}$
When $x = 1, V (1) = 9 volt$
When $x = - 2, V (- 2) = 24 volt$
$∴ ΔV = V (- 2) - V (1) = 15 volt E = - \frac{ΔV}{Δx} = - 10 x E at x = - 1 m will be - 10 \times (- 1) = + 10 N / C$
$∴ F = qE = + (1) (10) = + 10 N$ along positive x-axis.

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