We know that electric field (E ) at any point in space can be calculated using the relation
`vecE = - (deltaV)/(deltax)hati - (deltaV)/(deltay)hatj - (deltaV)/(deltaz)hatk`

if we know the variation of potential (V) at that point. Now let the electric potential in volt along the x-axis vary as `V = 2x^2`, where x is in meter. Its variation is as shown in figure
Draw the variation of electric field (E ) along the x-axis.

Options

A.
B.
C.
D.

Answer

C

Explanation

`E=-(dV)/(dx)=-4x`
`F=qE=2.5xx10^(-6)(-4x)=-10^(-5)x`
`W=underset(2)overset(0)int Fdx=-10^(-5)underset(2)overset(0)intxdx`
`(1)/(2)mv^(2)=10^(-5)[(x^(2))/(2)]_(0)^(2)` or `V=2ms^(-1)`