CGPET 2021 Solved Paper

If ∆V is the potential difference and ∆x is the effective displacement between two points, then the electric field is related with the potential as
E=

−∆V

∆x

‌or‌E=−

dV

dx

i.e. Negative rate of change of potential is equal to the electric fields.
Ex=−

dV

dx

=

−d

dx

(−kxy)=+ky .....(i)
and along Y - axis,
Ey=−

dV

dy

=

−d

dy

(−kxy)=+kx .....(ii)
∴ Resultant electric field,

Put the values from eq. (i) and (ii), we get
E=√(ky)2+(kx)2
⇒ E=k√x2+y2 .....(iii)
From eq. (iii), we get
E=k√r2=kr
∴ E∝r