An electric field hatE= 30 x2 hati exists in space. Then, the potential difference VA - V0 , where V0 is the potential at the origin and VA is the potential at x = 2 m , is given by

Question

An electric field hatE= 30 x2 hati exists in space. Then, the potential difference VA - V0 , where V0 is the potential at the origin and VA is the potential at x = 2 m , is given by (A)  -80 hatj  (B)  120 hatj  (C)  -120 hatj  (D)  80 hatj

Tardigrade Admin · Accepted Answer

As we know, the relation between electric field and potential difference is given as

v_{0} \int v_{A} = - 0 \int r B \cdot d r

\Rightarrow V_{A} - V_{0} = - 0 \int 2 m 30 x^{2} d x

= - 30 [\frac{x ^{3}}{3}]_{0}^{2}

\Rightarrow V_{A} - V_{0} = - 30 \times [\frac{2 ^{3}}{3} - \frac{0}{3}]

= - 30 \times \frac{8}{3}

= - 80 V

Note Potential is a scalar quantity. So, it cannot be written as

- 80 \hat{j}

as given in option.

Q. An electric field $\hat{E} = 30 x^{2} \hat{i}$ exists in space. Then, the potential difference $V_{A} - V_{0}$ , where $V_{0}$ is the potential at the origin and $V_{A}$ is the potential at $x = 2 m$ , is given by

$- 80 \hat{j}$

$120 \hat{j}$

$- 120 \hat{j}$

$80 \hat{j}$

Q. An electric field E^=30x2i^ exists in space. Then, the potential difference VA​−V0​ , where V0​ is the potential at the origin and VA​ is the potential at x=2m , is given by

−80j^​

120j^​

−120j^​

80j^​

Q. An electric field $\hat{E} = 30 x^{2} \hat{i}$ exists in space. Then, the potential difference $V_{A} - V_{0}$ , where $V_{0}$ is the potential at the origin and $V_{A}$ is the potential at $x = 2 m$ , is given by

$- 80 \hat{j}$

$120 \hat{j}$

$- 120 \hat{j}$

$80 \hat{j}$