A uniform electric field having strength $\to E$ is existing in x-y plane as shown in figure. Find the potential difference between origin O and A $(d, d, 0)$ :

$- E d (cos θ + sin θ)$
$E d (cos θ - sin θ)$
$\sqrt{2} E d$
none of these

Question

A uniform electric field having strength $\to E$ is existing in x-y plane as shown in figure. Find the potential difference between origin O and A $(d, d, 0)$ :

$- E d (cos θ + sin θ)$
$E d (cos θ - sin θ)$
$\sqrt{2} E d$
none of these

Toppr Admin · Accepted Answer

Here - -x2192-E-Ecos-x3B8-i-Esin-x3B8-jPotential-V-x2212-x222B-d-d-0-0-0-0-x2192-E-x2192-dr-x2212-x222B-d-d-0-0-0-0-Ecos-x3B8-i-Esin-x3B8-j-dx-i-dy-j-x2212-Ecos-x3B8-x222B-d0dx-Esin-x3B8-x222B-d0dy-x2212-Ed-cos-x3B8-sin-x3B8-

A uniform electric field having strength →E is existing in x-y plane as shown in figure. Find the potential difference between origin O and A (d,d,0):−Ed(cosθ+sinθ)Ed(cosθ−sinθ)√2Ednone of these

Here , →E=Ecosθ^i+Esinθ^jPotential,V=−∫(d,d,0)(0,0,0)→E.→dr=−∫(d,d,0)(0,0,0)(Ecosθ^i+Esinθ^j).(dx^i+dy^j)=−[Ecosθ∫d0dx+Esinθ∫d0dy]=−Ed(cosθ+sinθ)

A uniform electric field having strength $\to E$ is existing in x-y plane as shown in figure. Find the potential difference between origin O and A $(d, d, 0)$ :

$- E d (cos θ + sin θ)$
$E d (cos θ - sin θ)$
$\sqrt{2} E d$
none of these

Here , $\to E = E cos θ^i + E sin θ^j$
Potential, $V = - \int_{(0, 0, 0)}^{(d, d, 0)} \to E . \to d r$

$= - \int_{(0, 0, 0)}^{(d, d, 0)} (E cos θ^i + E sin θ^j) . (d x^i + d y^j) = - [E cos θ \int_{0}^{d} d x + E sin θ \int_{0}^{d} d y]$

$= - E d (cos θ + sin θ)$