An electric field vecE=A x hati exists in the space, where A=10 V / m 2. Consider the potential at (10 m , 20 m ) to be zero. The potential (in V ) at the origin is .

Question

An electric field vecE=A x hati exists in the space, where A=10 V / m 2. Consider the potential at (10 m , 20 m ) to be zero. The potential (in V ) at the origin is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Figure shows the situation described in question. Here

BC

is the equipotential line so we can use

V_{C} = V_{B} = 0

If

V_{0}

be the potential at the origin, we can use

V_{0} - V_{B} = A \int B E d x = 0 \int 10 A x d x

\Rightarrow V_{0} - 0 = A ∣ ∣ \frac{x ^{2}}{2} ∣ ∣_{0}^{10} = 10 \times \frac{1 0 ^{2}}{2} = 500 V

Q. An electric field E=Axi^ exists in the space, where A=10V/m2. Consider the potential at (10m,20m) to be zero. The potential (in V ) at the origin is _______.

Figure shows the situation described in question. Here BC is the equipotential line so we can use VC​=VB​=0 If V0​ be the potential at the origin, we can use V0​−VB​=A∫B​Edx=0∫10​Axdx ⇒V0​−0=A∣∣​2x2​∣∣​010​=10×2102​=500V

Q. An electric field $E = A x \hat{i}$ exists in the space, where $A = 10 V / m^{2}$ . Consider the potential at $(10 m, 20 m)$ to be zero. The potential (in $V$ ) at the origin is _______.