A square of side x m lies in the x-y plane in a region, where the magnetic field is given by vecB=B0(3 hati+4 hatj+5 hatk)T, where B0 is constant. The magnitude of flux passing through the square is

Question

A square of side x m lies in the x-y plane in a region, where the magnetic field is given by vecB=B0(3 hati+4 hatj+5 hatk)T, where B0 is constant. The magnitude of flux passing through the square is (A) 5B0 x2 Wb (B) 3B0 x2 Wb (C) 2B0 x2 Wb (D) B0 x2 Wb

Tardigrade Admin · Accepted Answer

Here, vecA=x2 hatk m2 and vecB=B0(3 hati+4 hatj+5 hatk)T As φ= vecB⋅ vecA=B0(3 hati+4 hatj+5 hatk)⋅ x2 hatk ∴ φ=5B0 x2 Wb

Q. A square of side $x m$ lies in the $x$ - $y$ plane in a region, where the magnetic field is given by $B = B_{0} (3 \hat{i} + 4 \hat{j} + 5 \hat{k}) T$ , where $B_{0}$ is constant. The magnitude of flux passing through the square is

$5 B_{0} x^{2} Wb$

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

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

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

Here, $A = x^{2} \hat{k} m^{2}$ and $B = B_{0} (3 \hat{i} + 4 \hat{j} + 5 \hat{k}) T$
As $ϕ = B \cdot A = B_{0} (3 \hat{i} + 4 \hat{j} + 5 \hat{k}) \cdot x^{2} \hat{k}$
$∴ ϕ = 5 B_{0} x^{2} Wb$

Q. A square of side xm lies in the x-y plane in a region, where the magnetic field is given by B=B0​(3i^+4j^​+5k^)T, where B0​ is constant. The magnitude of flux passing through the square is

5B0​x2Wb

3B0​x2Wb

2B0​x2Wb

B0​x2Wb