Important Derivations: Moving Charges and Magnetism

# Important Derivations: Moving Charges and Magnetism | Physics Class 12 - NEET PDF Download

(1) Biot Savarts Law

With the help of experimental results, Biot and Savart arrived at a mathematical expression that gives

the magnetic field at some point in space in terms of the current that produces the field.

Experimentally, it was found that, magnetic field at point P varies as:
(1)
(2)

here
(permeability of free space)
Unit of B: T or Wb/m2
Scalar Form

Vector Form

(2) The parallel coaxial circular coils of equal radius R and equal number of turns N carry equal currents I in the same direction and are separated by a distance 2 R. Find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres.

To find the magnitude and direction of the net magnetic field at the midpoint of the line joining the centers of two parallel coaxial circular coils, we can use the principle of superposition.

Let’s consider the two circular coils, Coil 1 and Coil 2, carrying equal currents I in the same direction. They have equal radii R and are separated by a distance of 2R. The midpoint of the line joining their centers is the point where we want to find the net magnetic field.

At the midpoint, the magnetic field produced by Coil 1 and Coil 2 will add together to give the net magnetic field.

The magnetic field (B1) produced at the midpoint due to Coil 1 can be calculated using the formula for the magnetic field at the center of a circular coil:

where: μ0 = Permeability of free space (4π×10−7T⋅m/A),
N = Number of turns in each coil (since they have equal turns, N is the same for both coils),
I = Current flowing through each coil,
R = Radius of each coil.

The magnetic field (B2) produced at the midpoint due to Coil 2 is the same as B1 since both coils are identical and carry the same current.
Now, to find the net magnetic field (Bnet) at the midpoint, we add the contributions from both coils:

So, the magnitude of the net magnetic field at the midpoint is  The direction of the net magnetic field is along the axis of the coils, which is the line joining their centers. It points from Coil 1 to Coil 2.
Therefore, the magnitude of the net magnetic field is  and its direction is along the axis of the coils from Coil 1 to Coil 2.

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## Physics Class 12

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## FAQs on Important Derivations: Moving Charges and Magnetism - Physics Class 12 - NEET

 1. What is the formula to calculate the magnetic field due to a long straight wire?
Ans. The formula to calculate the magnetic field due to a long straight wire is given by the Biot-Savart law: B = (μ₀I)/(2πr), where B is the magnetic field, μ₀ is the permeability of free space, I is the current flowing through the wire, and r is the distance from the wire.
 2. How can the direction of the magnetic field due to a current-carrying wire be determined?
Ans. The direction of the magnetic field due to a current-carrying wire can be determined using the right-hand rule. If the thumb of the right hand points in the direction of the current, then the curled fingers indicate the direction of the magnetic field around the wire.
 3. What is Ampere's circuital law?
Ans. Ampere's circuital law states that the line integral of the magnetic field around a closed loop is equal to the product of the permeability of free space and the total current passing through the loop. Mathematically, it can be written as ∮B·dl = μ₀I, where B is the magnetic field, dl is an infinitesimal length element along the closed loop, μ₀ is the permeability of free space, and I is the current passing through the loop.
 4. Explain the working principle of a cyclotron.
Ans. A cyclotron is a device used to accelerate charged particles. It consists of two hollow D-shaped electrodes called dees, placed in a magnetic field. The charged particles are injected into the center of the cyclotron and are accelerated by an alternating electric field between the dees. As the particles gain energy, they move in a circular path due to the magnetic field. The radius of the circular path increases with the energy of the particles, allowing them to be accelerated to high speeds.
 5. What is the force experienced by a current-carrying conductor placed in a magnetic field?
Ans. A current-carrying conductor placed in a magnetic field experiences a force known as the magnetic force. The magnitude of this force can be calculated using the formula F = BILsinθ, where F is the force, B is the magnetic field, I is the current flowing through the conductor, L is the length of the conductor in the magnetic field, and θ is the angle between the direction of the current and the magnetic field.

## Physics Class 12

105 videos|425 docs|114 tests

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