Charge Q is given a displacement vecr=a hati+b hatj in an electric field vecE=E1 hati+E2 hatj . The work done is

Question

Charge Q is given a displacement vecr=a hati+b hatj in an electric field vecE=E1 hati+E2 hatj . The work done is (A) Q(E1 a+E2 b) (B) Q √(E1 a)2+(E2 b)2 (C) Q(E1+E2) √a2+b2 (D) Q √(E12+E22) √a2+b2

Tardigrade Admin · Accepted Answer

W= vecF ⋅ vecr=(Q vecE) ⋅( vecr)=Q(E1 hati+E2 hatj) ⋅(a hati+b hatj) =Q E1 a+Q E2 b

Q. Charge $Q$ is given a displacement $r = a \hat{i} + b \hat{j}$ in an electric field $E = E_{1} \hat{i} + E_{2} \hat{j} .$ The work done is

$Q (E_{1} a + E_{2} b)$

$Q (E_{1} a)^{2} + (E_{2} b)^{2}$

$Q (E_{1} + E_{2}) a^{2} + b^{2}$

$Q (E_{1}^{2} + E_{2}^{2}) a^{2} + b^{2}$

$W = F \cdot r = (Q E) \cdot (r) = Q (E_{1} \hat{i} + E_{2} \hat{j}) \cdot (a \hat{i} + b \hat{j})$
$= Q E_{1} a + Q E_{2} b$

Q. Charge Q is given a displacement r=ai^+bj^​ in an electric field E=E1​i^+E2​j^​. The work done is

Q(E1​a+E2​b)

Q(E1​a)2+(E2​b)2​

Q(E1​+E2​)a2+b2​

Q(E12​+E22​)​a2+b2​