An electric field vec E-25hat i-30hat j-NC-1- exists in a region of space- If the potential the origin is taken to be zero then the potential x-2 m- y-2m is-110 J-140 J-130 J-120 J

Question

Toppr Admin · Accepted Answer

Potential difference between two points $Δ V =$ work done per unit charge $= \frac{\int \to F . \to d r}{q} = \frac{\int q \to E . \to d r}{q}$
$Δ V = - \int \to E . \to d r$ ...(i)
$E = 25^i + 30^j$ and coordinates of given point $\to r = 2^i + 2^j \to d r = d x^i + d y^j$ substituting values in equation (i)
$Δ V = - \int_{\to 0}^{\to r} 25^i + 30^j . d x^i + d y^j$
$Δ V = - \int_{0}^{2} 25 d x + \int_{0}^{2} 30 d y$

$= [25 x]_{0}^{2} + [[30 y]_{0}^{2}$

$= 50 + 60 = - 110 V$

$V - V_{o r i g i n} = - 110 J$ given $V_{o r i g i n} = 0$
$V = - 110 J$ hence correct answer is option A

An electric field →E=(25^i+30^j)NC−1 exists in a region of space. If the potential at the origin is taken to be zero then the potential at x=2m,y=2m is−110J−140J−130J−120J

An electric field $\to E = (25^i + 30^j) N C^{- 1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x = 2 m, y = 2 m$ is
$- 110 J$
$- 140 J$
$- 130 J$
$- 120 J$