Assume that an electric field vecE=30 x2 hati exists in space. Then the potential difference VA-VO' where VO is the potential at the origin and VA the potential at x=2 m is

Question

Assume that an electric field vecE=30 x2 hati exists in space. Then the potential difference VA-VO' where VO is the potential at the origin and VA the potential at x=2 m is (A) 120 J (B) -120 J (C) -80 J (D) 80 J

Tardigrade Admin · Accepted Answer

dV=- vecE ⋅ overlined x ∫ limitsV0VA d V=-∫ limits02 30 x2 d x VA-VO=-[10 x3]02=-80 J

Q. Assume that an electric field $E = 30 x^{2} \hat{i}$ exists in space. Then the potential difference $V_{A} - V_{O^{'}}$ where $V_{O}$ is the potential at the origin and $V_{A}$ the potential at $x = 2 m$ is

120 J

-120 J

-80 J

80 J

$d V = - E \cdot \overline{d x}$
$V_{0} \int V_{A} d V = - 0 \int 2 30 x^{2} d x$
$V_{A} - V_{O} = - [10 x^{3}]_{0}^{2} = - 80 J$

Q. Assume that an electric field E=30x2i^ exists in space. Then the potential difference VA​−VO′​ where VO​ is the potential at the origin and VA​ the potential at x=2m is