A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by vecB= B0 (2 hati + 3 hatj +4 hatk)T where B0 is constant. The magnitude of flux passing through the square is

Question

A square of side L meters lies in the x-y plane in a region, where the magnetic field is given by vecB= B0 (2 hati + 3 hatj +4 hatk)T where B0 is constant. The magnitude of flux passing through the square is (A) 2B0 L2Wb (B) 3B0 L2Wb (C) 4B0 L2Wb (D) √29B0L2Wb

Tardigrade Admin · Accepted Answer

Here, vecB = B0 (2 hati +3 hatj +4 hatk) T Area of the square = L2 hatk m2 ∴ Flux passing through the square, φ = vecB ⋅ vec A =B0 (2 hat i + 3 hat j + 4 hat k) ⋅ L2 hat k = 4 B0 L2 Wb

Q. A square of side $L$ meters lies in the $x - y$ plane in a region, where the magnetic field is given by
$B = B_{0} (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) T$
where $B_{0}$ is constant. The magnitude of flux passing through the square is

$2 B_{0} L^{2} Wb$

$3 B_{0} L^{2} Wb$

$4 B_{0} L^{2} Wb$

$29 B_{0} L^{2} Wb$

Here, $B = B_{0} (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) T$
Area of the square $= L^{2} \hat{k} m^{2}$
$∴$ Flux passing through the square,
$ϕ = B \cdot A = B_{0} (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) \cdot L^{2} \hat{k}$
$= 4 B_{0} L^{2} Wb$

Q. A square of side L meters lies in the x−y plane in a region, where the magnetic field is given by B=B0​(2i^+3j^​+4k^)T where B0​ is constant. The magnitude of flux passing through the square is

2B0​L2Wb

3B0​L2Wb

4B0​L2Wb

29​B0​L2Wb