A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of , (i) an equilateral tringle of side 'a' (ii) A square of side 'a' The magnetic dipole moments of the coil in each case respectively are :

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Magnetism and Matter question

2021 · Q165

Magnetism and Matter question

2021 · Q165

View written solutionFree

Correct answer: B

NEET 2021 Physics - Magnetism and Matter Question 12 English Explanation 1

x = \sqrt {{a^2} - {{{a^2}} \over 4}} = \sqrt {{{3{a^2}} \over 4}} = \sqrt {{{3{a^2}} \over 4}} = {{\sqrt 3 } \over 2}a

{A_1} = {1 \over 2} \times a \times {{\sqrt 3 } \over 2}a

{A_1} = {{\sqrt 3 } \over 4}{a^2}

{\mu _1} = {N_1}I{A_1}

{\mu _1} = {{4I\sqrt 3 } \over 4}{a^2}

{\mu _1} = \sqrt 3 I{a^2}

NEET 2021 Physics - Magnetism and Matter Question 12 English Explanation 2

{A_2} = {a^2}

{\mu _2} = {N_2}I{A_2}

= 3 \times I \times {a^2}

{\mu _2} = 3I{a^2}

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Magnetism and Matter question

2021 · Q165

Magnetism and Matter question

2021 · Q165

View written solutionFree

Correct answer: B

x = \sqrt {{a^2} - {{{a^2}} \over 4}} = \sqrt {{{3{a^2}} \over 4}} = \sqrt {{{3{a^2}} \over 4}} = {{\sqrt 3 } \over 2}a

{A_1} = {1 \over 2} \times a \times {{\sqrt 3 } \over 2}a

{A_1} = {{\sqrt 3 } \over 4}{a^2}

{\mu _1} = {N_1}I{A_1}

{\mu _1} = {{4I\sqrt 3 } \over 4}{a^2}

{\mu _1} = \sqrt 3 I{a^2}

{A_2} = {a^2}

{\mu _2} = {N_2}I{A_2}

= 3 \times I \times {a^2}

{\mu _2} = 3I{a^2}