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 triangle of side a (ii) a square of side a The magnetic dipole moments of the coils in each case respectively are – I is the current through the coils. (a) 4Ia² and 3Ia² (b) √3Ia² and 3Ia² (c) 3Ia² and Ia² (d) 3Ia² and 4Ia²
By BYJU'S Exam Prep
Updated on: September 13th, 2023
Step I – It is given
12a is the length of uniform conducting wire
R is the resistance of a wire
I is the current through the coils
Step II – Formula to be used
The magnetic dipole moment of the coil is written as
µ = NiA
Where µ is the magnetic moment,
N is the total number of turns in the wire
i is the current in the coil
A is the area of cross-section
Table of content
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1.
A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil in the shape of –
-
2.
(i) an equilateral triangle of sides a
-
3.
(ii) a square of side a
-
4.
The magnetic dipole moments of the coils in each case respectively are –
-
5.
I is the current through the coils.
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6.
(a) 4Ia² and 3Ia2
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7.
(b) √3Ia2 and 3Ia2
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8.
(c) 3Ia2 and Ia2
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9.
(d) 3Ia2 and 4Ia2
We know that
N = Total length of the wire/ Length of each turn
Step III – To calculate the magnetic dipole moment when the current carrying coil is an equilateral triangle shape
a is the side of an equilateral triangle
Length of equilateral triangular turn = a + a + a = 3a
Number of total triangular turns in the wire N = 12a/3a = 4
Area of equilateral triangle A = √3/4 x side2
Magnetic dipole moment µ = 4 x I x √3/4 x a2 = √3Ia2
Step IV – To calculate the magnetic dipole moment when the current carrying coil is a square shape
a is the side of the square
Length of square coil = a + a + a + a = 4a
Number of total square turns in the wire N = 12a/4a = 3
Area of square A = side2
Magnetic dipole moment µ = 3 x I x a2 = 3Ia2
Therefore, the magnetic moment in the first case is √3Ia2 and the magnetic moment in the second case is 3Ia2.
Summary:
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 triangle of sides a
(ii) a square of side a
The magnetic dipole moments of the coils in each case respectively are –
I is the current through the coils.
(a) 4Ia² and 3Ia2
(b) √3Ia2 and 3Ia2
(c) 3Ia2 and Ia2
(d) 3Ia2 and 4Ia2
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 triangle of side a
(ii) a square of side a
The magnetic dipole moments of the coils in each case respectively are –
I is the current through the coils.
(b) √3la2 and 3Ia2.
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