SATHEE: Moving Charges and Magnetism

Moving Charges and Magnetism - Result Question 47

48. A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be

(a) $2 : 1$

(b) $1 : 4$

(d) $1 : 2$

[1998]

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Answer:

Correct Answer: 48. (b)

Solution:

(b) Let $ℓ$ be length of wire.

Ist case : $ℓ = 2 π r \Rightarrow r = \frac{ℓ}{2 π}$

$B = \frac{μ_{0} I n}{2 r} = \frac{μ_{0} I \times 2 π}{2 ℓ} = \frac{μ_{0} π I}{ℓ} [∵ n = 1] \dots (1)$

2nd Case $: ℓ = 2 (2 π r^{'}) \Rightarrow r^{'} = \frac{ℓ}{4 π}$

$B^{'} = \frac{μ_{0} I n}{2 \frac{ℓ}{4 π}} = \frac{2 μ_{0} I π}{\frac{ℓ}{2}} = 4 (\frac{μ_{0} π I}{ℓ}) = 4 B$ ,

using (1) (where $n = 2$ )

If a current carrying circular loop $(n = 1)$ is turned into a coil having $n$ identical turns then magnetic field at the centre of the coil becomes $n^{2}$ times the previous field i.e., $B_{(n turn)} = n^{2} B_{(single turn)}$

Moving Charges and Magnetism - Result Question 47

48. A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be

Answer:

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Moving Charges and Magnetism - Result Question 47

48. A coil of one turn is made of a wire of certain length and then from the same length a coil of two turns is made. If the same current is passed in both the cases, then the ratio of the magnetic inductions at their centres will be

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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