Question

The electric potential decreases uniformly from 120 V to 80 V as one moves on the x-axis from $x=-1cm$ to $x=+1cm$. The electric field at the origin.

• A. must be equal to 20 Vcm${}^{-1}$
• B. must be equal to 20 Vm${}^{-1}$
• C. greater than or equal to 20 Vcm${}^{-1}$
• D. may be less than 20 Vcm${}^{-1}$

Answer 1

The correct option is C greater than or equal to 20 Vcm${}^{-1}$

$dv=-\overrightarrow{E}.\overrightarrow{d}x=-Edx\cos \theta$

$E=-\frac{dV}{\cos \theta dx}$

$\cos \theta \approx 1$, if we take $\cos \theta =1$,then

$E_{min}=-\frac{80-120}{1-(-1)}=\frac{40}{2}=20Vc{m}^{-1}$

Hence E would be greater than or equal to $20$