An electric field (-30 hati+20 hatj) V m -1 exists in space. If the potential at the origin is zero, then find the potential (in volt) at (5 m , 3 m ).

Question

An electric field (-30 hati+20 hatj) V m -1 exists in space. If the potential at the origin is zero, then find the potential (in volt) at (5 m , 3 m ). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

d V =- vecE ⋅ d vecr=-(-30 hati+20 hatj) ⋅(d x hati+d y hatj+d z hatk) =30 d x-20 d y ⇒ ∫ limits0V d V=∫ limits(0,0)(5,3)(30 d x-20 d y) ⇒ V=(30 x)05-(20 y)03 =150-60=90 V

Q. An electric field $(- 30 \hat{i} + 20 \hat{j}) V m^{- 1}$ exists in space. If the potential at the origin is zero, then find the potential (in volt) at $(5 m, 3 m)$ .

$d V = - E \cdot d r = - (- 30 \hat{i} + 20 \hat{j}) \cdot (d x \hat{i} + d y \hat{j} + d z \hat{k})$
$= 30 d x - 20 d y$
$\Rightarrow 0 \int V d V = (0, 0) \int (5, 3) (30 d x - 20 d y)$
$\Rightarrow V = (30 x)_{0}^{5} - (20 y)_{0}^{3}$
$= 150 - 60 = 90 V$

Q. An electric field (−30i^+20j^​)Vm−1 exists in space. If the potential at the origin is zero, then find the potential (in volt) at (5m,3m).

dV=−E⋅dr=−(−30i^+20j^​)⋅(dxi^+dyj^​+dzk^) =30dx−20dy ⇒0∫V​dV=(0,0)∫(5,3)​(30dx−20dy) ⇒V=(30x)05​−(20y)03​ =150−60=90V

Q. An electric field $(- 30 \hat{i} + 20 \hat{j}) V m^{- 1}$ exists in space. If the potential at the origin is zero, then find the potential (in volt) at $(5 m, 3 m)$ .

$d V = - E \cdot d r = - (- 30 \hat{i} + 20 \hat{j}) \cdot (d x \hat{i} + d y \hat{j} + d z \hat{k})$
$= 30 d x - 20 d y$
$\Rightarrow 0 \int V d V = (0, 0) \int (5, 3) (30 d x - 20 d y)$
$\Rightarrow V = (30 x)_{0}^{5} - (20 y)_{0}^{3}$
$= 150 - 60 = 90 V$