Question

A square of side L meters lies in the x-y plane in a region where the magnetic field is given by $\overline{B}=B_0(2\hat{i}+3\hat{j}+4\hat{k})T$,where $B_0$ is constant. The magnitude of flux passing through the square is:

• A. $8B_0{L}^{2}Wb$
• B. $12B_0{L}^{2}Wb$
• C. $4B_0{L}^{2}Wb$
• D. $\sqrt{4\times 29}{B}_{0}Wb$

Answer 1

The correct option is C $4B_0{L}^{2}Wb$

Area vector $=\overrightarrow{A}=L^2\hat{k}$ ...(Perpendicular to x-y plane)

Magnetic field vector$,\overrightarrow{B}=B_0(2\hat{i}+3\hat{j}+4\hat{k})T$

$\varphi =\overrightarrow{B}.\overrightarrow{A}$

$\varphi =B_0(2\hat{i}+3\hat{j}+4\hat{k}).L^2\hat{k}$

$\varphi =B_0(2L^2\hat{i}.\hat{k}+3L^2\hat{j}.\hat{k}+4L^2\hat{k}.\hat{k})$

$\because \hat{i}.\hat{k}=0$ & $\hat{j}.\hat{k}=0$ & $\hat{k}.\hat{k}=1$

$\therefore \varphi =B_{0}4L^2$

$\therefore \varphi =4B_0{L}^{2}wb$

where $L=$ length of side of square