An electric field vecE=E0 hati+E0 hatj exists in space. The flux through a triangular loop with vertices at ((a/2), 0,0), ((a/2), 0, a) and ((a/2), a, (a/2)) is (E0 a2/b) . Find b

Question

An electric field vecE=E0 hati+E0 hatj exists in space. The flux through a triangular loop with vertices at ((a/2), 0,0), ((a/2), 0, a) and ((a/2), a, (a/2)) is (E0 a2/b) . Find b (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The flux of y-component of vecE is zero through this loop. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/fc8fb07d7cebc8ba9040cd426a855607-.png" /> ∴ φ=E0 × (1/2) × a × a=φ=(E0 a2/2)

Q. An electric field $E = E_{0} \hat{i} + E_{0} \hat{j}$ exists in space. The flux through a triangular loop with vertices at $(\frac{a}{2}, 0, 0)$ , $(\frac{a}{2}, 0, a)$ and $(\frac{a}{2}, a, \frac{a}{2})$ is $\frac{E _{0} a ^{2}}{b} .$ Find $b$

The flux of $y$ -component of $E$ is zero through this loop.

$∴ ϕ = E_{0} \times \frac{1}{2} \times a \times a = ϕ = \frac{E _{0} a ^{2}}{2}$

Q. An electric field E=E0​i^+E0​j^​ exists in space. The flux through a triangular loop with vertices at (2a​,0,0), (2a​,0,a) and (2a​,a,2a​) is bE0​a2​. Find b

The flux of y-component of E is zero through this loop. ∴ϕ=E0​×21​×a×a=ϕ=2E0​a2​

Q. An electric field $E = E_{0} \hat{i} + E_{0} \hat{j}$ exists in space. The flux through a triangular loop with vertices at $(\frac{a}{2}, 0, 0)$ , $(\frac{a}{2}, 0, a)$ and $(\frac{a}{2}, a, \frac{a}{2})$ is $\frac{E _{0} a ^{2}}{b} .$ Find $b$

The flux of $y$ -component of $E$ is zero through this loop.

$∴ ϕ = E_{0} \times \frac{1}{2} \times a \times a = ϕ = \frac{E _{0} a ^{2}}{2}$