The force between two parallel currents, also known as Ampere's law, is a fundamental concept in NCERT Class 12 Physics. Ampere's law describes how two parallel current-carrying conductors interact with each other due to the magnetic fields they produce. This interaction results in a force between the two conductors.
Ampere's Law
Let's break down the concept of Ampere's law.
Current-Carrying Conductors: To understand Ampere's law, we first need two parallel current-carrying conductors. These conductors can be wires or any other suitable objects that allow electric current to flow through them.
Magnetic Fields: When an electric current flows through a conductor, it generates a magnetic field around it. This magnetic field can be visualised using the right-hand rule. If you curl your right hand around the conductor with your thumb pointing in the direction of the current flow, your fingers will wrap around the conductor in the direction of the magnetic field lines.
Force between Parallel Currents: When two current-carrying conductors are placed parallel to each other, their magnetic fields interact. If the currents are in the same direction, the magnetic fields reinforce each other, and if they are in opposite directions, the fields oppose each other. This interaction of magnetic fields results in a force between the conductors.
Magnitude of the Force: The magnitude of the force between two parallel currents can be calculated using Ampere's law, which is given by:
F = (μ₀ I₁ I₂ L) / (2π d)
Where:
F is the force between the two conductors.
μ₀ is the permeability of free space, a fundamental constant in electromagnetism.
I₁ and I₂ are the currents in the two conductors.
L is the length of the conductors over which the currents flow.
d is the separation distance between the conductors.
Direction of the Force: The direction of the force can be determined using the right-hand rule. If the currents are in the same direction, the conductors are attracted to each other, and if the currents are in opposite directions, they repel each other.
It's important to note that Ampere's law is a simplified formula that applies to long, straight conductors and assumes that the conductors are in a vacuum. In real-world situations, other factors, such as the shape of the conductors and the surrounding medium, may come into play, but this basic explanation provides a foundation for understanding the concept of the force between parallel currents.
FAQs on Force between two parallel currents, the ampere
Q.A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
Length of a side of the square coil, l = 10 cm = 0.1 m
Current flowing through the coil, I = 12 A
Number of turns of the coil, n = 20
Angle made by the plane of the coil with magnetic field, = 30
Strength of the magnetic field, B = 0.80 T
Magnitude of the magnetic torque experienced by the coil in the magnetic field is given by,
= nBIA, where A = Area of the square coil = 0.1
= 0.96 Nm
Q. Answer the following questions: (a) 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? (b) 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? (c) An electron travelling west to east enters a chamber having a uniform electrostatic field in 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.
- The initial velocity of the particle is either parallel or anti-parallel to the magnetic field. Hence, it travels along a straight path without suffering any deflection in the field.
- Yes, the final speed of the particle will be equal to its initial speed. This because magnetic force can change the direction of velocity, not its magnitude.
- This moving electron can remain undeflected if the electric force acting on it is equal and opposite of magnetic field. Magnetic force is directed towards the south. According to Fleming’s left hand rule, magnetic field should be applied in a vertically downward direction.
Q. The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?
Current in both the wires, I = 300 A
Distance between the wires, r = 1.5 cm = 0.015 m
Length of the two wires, l = 70 cm = 0.7 m
Now, force between the two wires is given by the relation:
F = , where = Permeability of free space = 4 T m
Hence F = N/m = 1.2 N/m
Since the direction of the current in the wires is opposite, a repulsive force exists between them.
Q.4.23 A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, (a) the wire intersects the axis, (b) the wire is turned from N-S to northeast-northwest direction, (c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
Magnetic field strength, B = 1.5 T
Radius of the cylindrical region, r = 10 cm = 0.1 m
Current in the wire passing through the cylindrical region, I = 7 A
- If the wire intersect the axis, then the length of the wire is the diameter of the cylindrical region, then l = 2r = 0.2 m
Angle between the magnetic field,
Magnetic force acting on the wire is given by the relation,
F = BIl = 1.5 = 2.1 N
Hence, a force of 2.1 N acts on the wire in a vertically downward direction.
- If the wire is turned from N-S to NE-NW direction, new length of the wire can be given as
Angle between magnetic field and current = 45
Force on the wire,
F = BI = BIl = 1.5 0.2 = 2.1 N
A vertically downward force of 2.1 N acts on the wire.
- When the wire is lowered from the axis by distance, d = 6.0 cm = 0.06 m
Let be the new length and is given by
= 4 (d + r) = 4(6 + 10) = 64
16 cm = 0.16 m
= BI = 1.5 = 1.68 N
The force acts vertically downwards.
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