The electric field in a certain region is given by E=(5 hati-3 hatj) kV / m. The potential difference (VB-VA) between points A and B, having coordinates (4,0,3) m and (10, 3,0) m respectively, is equal to

Question

The electric field in a certain region is given by E=(5 hati-3 hatj) kV / m. The potential difference (VB-VA) between points A and B, having coordinates (4,0,3) m and (10, 3,0) m respectively, is equal to (A) 21 kV (B) -21 kV (C) 39 kV (D) - 39 kV

Tardigrade Admin · Accepted Answer

Here, vecE=(5 hati-3 hatj) g V / m VB=VA=-∫ limitsrArB =-∫ limits(10,3,0)(4,0,3)(5 hati-3 hatj) ⋅(d x hati+d y hatj+d z hatk) =-5(10-4)+3(3-0) =-30+9 =-21 k V

Q. The electric field in a certain region is given by $E = (5 \hat{i} - 3 \hat{j}) kV / m$ . The potential difference $(V_{B} - V_{A})$ between points $A$ and $B$ , having coordinates $(4, 0, 3) m$ and $(10$ , $3, 0) m$ respectively, is equal to

21 kV

-21 kV

39 kV

- 39 kV

Here, $E = (5 \hat{i} - 3 \hat{j}) g V / m$
$V_{B} = V_{A} = - r_{A} \int r_{B}$
$= - (10, 3, 0) \int (4, 0, 3) (5 \hat{i} - 3 \hat{j}) \cdot (d x \hat{i} + d y \hat{j} + d z \hat{k})$
$= - 5 (10 - 4) + 3 (3 - 0)$
$= - 30 + 9$
$= - 21 kV$

Q. The electric field in a certain region is given by E=(5i^−3j^​)kV/m. The potential difference (VB​−VA​) between points A and B, having coordinates (4,0,3)m and (10, 3,0)m respectively, is equal to