Question

10A current carrying wire of length 1m is folded in a circular form .How many circular turns would produce the maximum magnetic moment ?
A. 1
B. 2
C. 4
D. Any value​

Answer 1

Answer:

0.25 is the correct answer

Answer 2

Given:

A current-carrying wire of length 1m is folded in a circular form

To find:

How many circular turns would produce the maximum magnetic moment?

Solution:

The length of the wire, L = 1 m

Let "r" represent the radius of the circular form.

The formula of the magnetic moment is given as:

μ = $\bold{NIA}$ ..... (i)

where

N = no. of turns

I = current across the coil

A = area of a circular coil

Since the wire of length 1 m is folded to form a circular form, therefore we can say that,

[Length of the wire] = N × [Circumference of the circular form]

⇒ L = N × [2 π r]

⇒ Nr = $\frac{L}{2\pi}$

substituting L = 1 m

⇒ Nr = $\frac{1}{2\pi}$

so we can say

⇒ N ∝ $\bold{\frac{1}{r}}$

∴ N ∝ $\bold{\frac{1}{A}}$ ..... [∵ A = πr²] ...... (ii)

Comparing (i) & (ii), we get

• If we increase the no. of turns of the coil then the area of the coil will decrease as its radius decreases.

• So, if N = 1 then r = 1 & A = π.
• Also, if N = 2 then r = $\frac{1}{2}$ & A = $\frac{\pi}{4}$ and so on.

Therefore, we can conclude that

$\boxed{\bold{The\: magnetic\: moment\: will\: be \:maximum \:when \:both\: N\: \&\: r\: is\: equal\: to\: 1.}}$

Thus, The final answer is the option (A) → 1 circular turn would produce the maximum magnetic moment.

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