Question

A loop, made of straight edges has six corners at A(0, 0, 0), B(L, 0, 0), C(L, L, 0), D(0, L, 0), E(0, L, L) and F(0, 0, L). A magnetic field = B0 () T is present in the region. The flux passing through the loop ABCDEFA (in that order) is

• A. B0L2 Wb
• B. 2 B0 L2 Wb
• C. $\sqrt { 2 }$ B0 $L ^ { 2 }$ Wb
• D. 4 B0 L2 Wb

Answer 1

Answer: (B)

2 B0 L2 Wb

Answer 2

here, $\overrightarrow { \mathrm { B } } = \mathrm { B } _ { 0 } ( \hat { \mathrm { i } } + \hat { \mathrm { k } } ) \mathrm { T }$

Area vector of ABCD $= L ^ { 2 } \hat { k }$

Area vector of DEFA $= L ^ { 2 } \hat { \mathbf { i } }$

Total area vector $\vec { A } = L ^ { 2 } ( \hat { i } + \hat { j } )$

Total magnetic flux

$\phi = \vec { B } \cdot \vec { A } = B _ { 0 } ( \hat { i } + \hat { j } ) \cdot L ^ { 2 } ( \hat { i } + \hat { k } )$