An electric field is given by Ex=-2 x3 hati N / C. The potential of the point (1,-2), if potential of the point (2,4) is taken as zero, is

Question

An electric field is given by Ex=-2 x3 hati N / C. The potential of the point (1,-2), if potential of the point (2,4) is taken as zero, is (A) -7.5 × 103 V (B) 7.5 × 103 V (C) -15 × 103 V (D) 15 × 103 V

Tardigrade Admin · Accepted Answer

d V=- vecE ⋅ d vecr=-(-2 x3 hati) ⋅(d x hati+d y hatj+d z hatk) =2 x3 d x ⇒ ∫ limits0V d V=∫ limits21(2 x3) × 103 d x V= -7.5 × 103 V

Q. An electric field is given by $E_{x} = - 2 x^{3} \hat{i} N / C$ . The potential of the point $(1, - 2)$ , if potential of the point $(2, 4)$ is taken as zero, is

$- 7.5 \times 1 0^{3} V$

$7.5 \times 1 0^{3} V$

$- 15 \times 1 0^{3} V$

$15 \times 1 0^{3} V$

$d V = - E \cdot d r = - (- 2 x^{3} \hat{i}) \cdot (d x \hat{i} + d y \hat{j} + d z \hat{k})$
$= 2 x^{3} d x$
$\Rightarrow 0 \int V d V = 2 \int 1 (2 x^{3}) \times 1 0^{3} d x$
$V = - 7.5 \times 1 0^{3} V$

Q. An electric field is given by Ex​=−2x3i^N/C. The potential of the point (1,−2), if potential of the point (2,4) is taken as zero, is

−7.5×103V

7.5×103V

−15×103V

15×103V