The solenoid and toroid are important topics in NCERT Class 12 Physics. Solenoids and toroids are both related to the behaviour of electric currents and magnetic fields. Let's break down these concepts:
Solenoid
A solenoid is a long, cylindrical coil of wire wound in the form of a helix. When an electric current flows through a solenoid, it generates a magnetic field around it. Solenoids are commonly used in various electrical and electromagnetic devices, such as electromagnets, relays, and doorbells.
Characteristics of Solenoids
- Magnetic Field: Inside the solenoid, the magnetic field lines run parallel to the axis of the coil. The field is strong and uniform inside the solenoid when the current is flowing.
- Direction of the Magnetic Field: The direction of the magnetic field inside the solenoid can be determined using the right-hand rule. If you curl your right-hand fingers around the solenoid in the direction of the current flow, your thumb points in the direction of the magnetic field.
- Magnetic Field Strength: The strength of the magnetic field inside a solenoid is directly proportional to the number of turns of the wire, the current flowing through the wire, and the permeability of the material inside the solenoid.
Solenoids are used in a wide range of applications, such as in electromagnetic locks, inductors, and actuators in various devices.
Toroid
A toroid is a doughnut-shaped or ring-shaped coil of wire. When an electric current flows through a toroid, it also generates a magnetic field, but the geometry and characteristics of this field are different from that of a solenoid. Toroids are often used in applications where a closed-loop magnetic circuit is required, such as in transformers and inductors.
Characteristics of Toroids
- Magnetic Field: The magnetic field produced by a toroid is confined within the core of the ring and does not escape into the surrounding space. This results in a highly efficient and strong magnetic field.
- Direction of the Magnetic Field: The direction of the magnetic field inside the toroid is primarily along the circular path within the core.
- Magnetic Field Strength: The strength of the magnetic field in a toroid depends on the number of turns of the wire, the current flowing through the wire, and the permeability of the core material.
Toroids are commonly used in transformers and inductors to transfer electrical energy from one coil to another or to store energy in the form of a magnetic field.
In summary, solenoids and toroids are both coil-shaped devices that use electric current to generate magnetic fields. Solenoids are typically linear coils used for various applications, while toroids are ring-shaped coils used for more specialized applications, particularly in transformers and inductors.
FAQs on Solenoid and Toroids
Q. A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
Length of the wire, l = 3 cm = 0.03 m
Current flowing in the wire, I = 10 A
Magnetic field, B = 0.27 T
Angle between current and the magnetic field, = 90
Magnetic force exerted on the wire is given as
F= BI = 0.27 = 8.1 N
Q. A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
Length of the solenoid, l = 80 cm = 0.8 m
Total number of turns in 5 layers, n = 5 = 2000
Diameter of the solenoid, D = 1.8 cm = 0.018 m
Current carrying by the solenoid, I = 8.0 A
Magnitude of the magnetic field inside the solenoid near its centre is given by the relation,
B = , where = permeability of free space = 4 Tm
B = = 2.51 T
Q. 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 m2. 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 round 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.
Magnetic field strength, B = 100 G = 100 T
Number of turns per unit length, n = 1000 turns / m
Current flowing in the coil, I = 15 A
= Permeability of free space = 4 T m
Magnetic field is given by the relation,
B = or nI = = = 7957.75 AA
If the length of the coil is taken as 50 cm , radius 4 cm, number of turns 400 and current 10 A, then these values are not unique for the given purpose. There is always a possibility of some adjustments with limits.
Q. 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 (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.
Inner radius of the toroid, = 25 cm = 0.25 m
Outer radius of the toroid, = 26 cm = 0.26 m
Number of turns on the coil, N = 3500
Current in the coil, I = 11 A
- Magnetic field outside a toroid is zero. It is non-zero only inside the core of a toroid.
- Magnetic field inside the core of a toroid is given by the relation,
B = . where = Permeability of free space = 4 T m
L = length of the toroid = 2) = (0.25 + 0.26)= 1.6022
B = = 3.0 T
- Magnetic field in the empty space surrounded by the toroid is zero.
Q. A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? g = 9.8 m s–2.
Length of the solenoid, L = 60 cm = 0.6 m
Radius of the solenoid, r = 4.0 cm = 0.04 m
It is given that there are 3 layers of windings of 300 turns each
Hence, total number of turns, n = 900
Length, l = 2 cm = 0.02 m
Mass of the wire, m = 2.5 g = 2.5 kg
Current flowing through the wire, I = 6 A
Acceleration due to gravity, g = 9.8 m/
We know, magnetic field produced inside the solenoid, B =
where = Permeability of free space = 4 T m
Magnetic force is given by the relation
F = Bil =
Also the force on the wire is equal to the weight of the wire, F = mg
mg =
I = = = 108 A
Hence, the current flowing through the solenoid is 108 A.
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