SATHEE: moving-charges-and-magnetism Question 21

moving-charges-and-magnetism Question 21

Question: Q. 16. A circular coil, having 100 turns of wire, of radius (nearly) $20 cm$ each, lies in the $X Y$ plane with its centre at the Origin of co-ordinates. Find the magnetic field at the point $(0, 0, 20 \sqrt{3} cm)$ when this coil carries a current of $(\frac{2}{π}) A$ .

A [Delhi Comptt. 2016]

Show Answer

Solution:

Ans. The plane of coil is $X Y$ plane and field point is on the Z-axis.

$∴$ Magnetic field on the axial point

$\begin{aligned} B & = \frac{μ_{0} I R^{2} N}{2 {(R^{2} + z^{2})}^{3 / 2}} & 1 & = \frac{4 π \times 10^{- 7} \times \frac{2}{π} \times (0.2)^{2} \times 100}{2 {[(0.2)^{2} + (0.2 \sqrt{3})^{2}]}^{3 / 2}} 1 / 2 & = \frac{8 \times 0.04 \times 10^{- 7} \times 100}{2 \times 0.04 \times 8 \times 0.2} & 1 / 2 & = 25 μ T & 1 / 2 \end{aligned}$

[CBSE Marking Scheme 2016]

?Long Answer Type Questions

(5 marks each)

[AI Q. 1. (i) Derive an expression for the magnetic field at point on the axis of a current carrying circular loop.

(ii) A coil of 100 turns (tightly bound) and radius 10 $cm$ , carries a current of $1 A$ . What is the magnitude of the magnetic field at the centre of the coil.

U] [SQP I 2017] Ans. (i) Derivation : 3 (ii) Numerical : 2 (i) Try yourself, Similar to 3 (b), Short Answer Type II

(ii) Since the coil is tightly bound, we may take each circular element to have the same radius $R = 10 cm = 0.1 m, N = 100$ Magnitude of magnetic field :

$\begin{aligned} B & = \frac{μ_{0} N I}{2 R} B & = \frac{4 π \times 10^{- 7} \times 10^{2} \times 1}{2 \times 10^{- 1}} & = 2 π \times 10^{- 4} & = 6.28 \times 10^{- 4} T \end{aligned}$

[CBSE Marking Scheme 2017]

Moving Charges And Magnetism

moving-charges-and-magnetism Question 21

?Long Answer Type Questions

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Moving Charges And Magnetism

moving-charges-and-magnetism Question 21

?Long Answer Type Questions

Table of Contents

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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