Question

hA square of side x m lies in the x-y plane in a region, where the magnetic field is given by $\overrightarrow { \mathrm { B } } = \mathrm { B } _ { 0 } ( 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } + 5 \hat { \mathrm { k } } )$ T, where B0 is constant. The magnitude of flux passing through the square is

• A. 5B0 x2 Wb
• B. 2*Bq x2* Wb
• C. 2B0 x2 Wb
• D. B0 x2 Wb

Answer 1

Answer: (A)

5B0 x2 Wb

Answer 2

Here , $\overrightarrow { \mathrm { A } } = \mathrm { x } ^ { 2 } \hat { \mathrm { k } } \mathrm { m } ^ { 2 }$ and

$\overrightarrow { \mathrm { B } } = \mathrm { B } _ { 0 } ( 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } + 5 \hat { \mathrm { k } } ) \mathrm { T }$

As $\phi = \overrightarrow { \mathrm { B } } \cdot \overrightarrow { \mathrm { A } } = \mathrm { B } _ { 0 } ( 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } + 5 \hat { \mathrm { k } } ) \cdot x ^ { 2 } \hat { \mathrm { k } }$

$\therefore \phi = 5 \mathrm {~B} _ { 0 } \mathrm { x } ^ { 2 } \mathrm {~Wb}$