Question

A 4 A current carrying loop consist of three identical quarter circles of radius 5 cm lying in the positive quadrants of the x-y, y-z and z-x planes with their centres at the origin joined together, value of at the origin is

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Answer 2

As $\overrightarrow { \mathrm { B } } = \overrightarrow { \mathrm { B } } _ { \mathrm { xy } } + \overrightarrow { \mathrm { B } } _ { \mathrm { yz } } + \overrightarrow { \mathrm { B } } _ { \mathrm { zx } }$ …….. (i)

Where

Substituting these values in equation (i) we get,

Here $\theta = \frac { \pi } { 2 } , \mathrm { I } = 4 \mathrm {~A}$and

$\therefore \overrightarrow { \mathrm { B } } = \frac { \mu _ { 0 } } { 4 \pi \mathrm { a } } \times \frac { 4 } { 5 \times 10 ^ { - 2 } } \times \frac { \pi } { 2 } ( \hat { \mathrm { i } } + \hat { \mathrm { j } } + \hat { \mathrm { k } } )$