Question

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

• A. $5B_{0}\, x^{2}\, Wb$
• B. $3B_{0}\, x^{2}\, Wb$
• C. $2B_{0}\, x^{2}\, Wb$
• D. $B_{0}\, x^{2}\, Wb$

Answer 1

Answer: (A)

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

Answer 2

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