A magnetic field of 100 G ( 1 G = 10 - 4 T ) is required, which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10 - 3 m 2 . The maximum current-carrying capacity of a given coil of wire is 15 A , and the number of turns per unit length that can be wound around a core is at most 1000 turns m - 1 . Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

Given that, Strength of magnetic field, B = 100 G = 100 × 10 - 4 T Number of turns per unit length, n = 1000 turns m - 1 Current flowing in the coil , I = 15 A Magnetic field is given by the relation, B = μ 0 n I , where μ 0 is the permeability of free space. ⇒ n I = B μ 0 = 100 × 10 - 4 4 π × 10 - 7 = 7957.74 ≈ 8000 A m - 1 . If the length of the coil is taken as 50 cm , radius 4 cm , the number of turns 400 and current 10 A , then we can achieve the required magnetic field. These values are not unique for the given purpose. There is always a possibility of some changes within limits.

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Two concentric circular coils X and Y of radii $16 cm$ and $10 cm$ , respectively, lie in the same vertical plane containing the north to south direction. Coil X has $20$ turns and carries a current of $16 A$ ; coil Y has $25 turns$ and carries a current of $18 A$ . The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

Important Questions on Moving Charges and Magnetism

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.15

A magnetic field of

100 G

(

1 G = 10^{- 4} T

) is required, which is uniform in a region of linear dimension about

10 cm

and area of cross-section about

10^{- 3} m^{2}

. The maximum current-carrying capacity of a given coil of wire is

μ_{0} =

, and the number of turns per unit length that can be wound around a core is at most

1000 turns m^{- 1}

. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

MEDIUM

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.16

For a circular coil of radius R and N turns carrying current I; the magnitude of the magnetic field at a point on its axis at a distance

x

from its centre is given by,

B = \frac{μ_{0} I R^{2} N}{2 {(X^{2} + R^{2})}^{\frac{3}{2}}}

Show that this reduces to the familiar result for the field at the centre of the coil.

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.16

Consider two parallel coaxial circular coils of equal radius

R

, and number of turns

N

, carrying equal currents in the same direction, and separated by a distance

R

. Show that the field on the axis around the midpoint between the coils is uniform over a distance that is small as compared to

R

, and is given by,

B = 0.72 \frac{μ_{0} N I}{R}

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.17

A toroid has a core (non-ferromagnetic) of inner radius

25 cm

and outer radius

26 cm

, around which

3500

turns of a wire are wound. If the current in the wire is

11 A

, what is the magnetic field outside the toroid, inside the core of the toroid? Take,

μ_{0} = 4 π \times 10^{- 7} H / m

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.18

A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.18

A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.18

An electron is moving west to east enters a chamber having a uniform electrostatic field in the north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight-line path.

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PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 4 - Moving Charges and Magnetism>ADDITIONAL EXERCISES>Q 4.19

An electron emitted by a heated cathode and accelerated through a potential difference of

2.0 kV

enters a region with the uniform magnetic field of

0.15 T

. Determine the trajectory of the electron if the field is transverse to its initial velocity.

Important Questions on Moving Charges and Magnetism

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