Untitled Quiz

Oersted's experiment proves that a magnetic field exists around any current-carrying conductor.
Magnetic fields can be described using lines of force, which are continuous closed curves.
Ampere's swimming rule helps determine the direction of the magnetic field, where the north pole of a magnetic needle deflects towards the left hand of a swimmer moving in the direction of the current.
The SI unit of magnetic field is Tesla (T), while the CGS unit is Gauss, with 1 Gauss = 10^-4 Tesla.

The Biot-Savart law calculates the magnetic field produced at a point by a current-carrying element.
It states that the magnetic field (dB) is directly proportional to the current (I), the length of the element (dl), and the sine of the angle (θ) between the current and the radius vector (r) connecting the element to the point, and inversely proportional to the square of the radial distance (r).

The magnetic field at a point due to a straight current-carrying conductor is given by: B = (μo * I / [(2 * π * r) * (sinφ1 + sinφ2)]) where μo is the permeability of free space, I is the current, r is the distance from the conductor, and φ1 and φ2 are the angles the lines joining the ends of the conductor to the point make with the perpendicular from the point to the conductor.
For an infinitely long conductor, the formula simplifies to: B = (μo * I) / (2 * π * r)

The magnetic field on the axis of a circular coil of radius r at a distance x from the center is given by: B = (μo * n * I * r^2) / [2 * (r^2 + x^2)^(3/2)] where n is the number of turns, and I is the current.
At the center of the coil, the magnetic field simplifies to: B = (μo * n * I) / (2 * r)

Every current-carrying loop acts as a magnetic dipole.
The magnetic moment (M) of a current-carrying loop is given by: |M| = N * I * A where N is the number of turns, I is the current, and A is the area of the loop.

Ampere's circuital law states that the line integral of magnetic field induction B around any closed path in a vacuum is equal to μo times the total current threading the closed path.
This law is applicable to closed paths of any size and shape.

A solenoid is a tightly wound helix of insulated copper wire.
The magnetic field inside a long solenoid is given by: B = μo * n * I where n is the number of turns per unit length and I is the current.
At the end of a long solenoid, the magnetic field is given by: B = μo * n * I / 2

A toroid is an endless solenoid shaped like a ring.
The magnetic field inside the turns of the toroid is constant and given by: B = μo * n * I where n is the number of turns per unit length and I is the current.
The magnetic field outside the toroid is zero.

Outside the cylinder (r > R): B = (μo * I) / (2 * π * r) where μo is the permeability of free space, I is the current, and r is the distance from the cylinder.
Inside the cylinder (r < R), assuming the current is uniformly distributed: B = (μo * μr * I * r) / (2 * π * R^2) where μr is the permeability of the cylinder's material.

The force acting on a charged particle (q) moving with velocity (v) in a uniform magnetic field (B) is given by: F = q (v × B)
The magnitude of this force is given by: |F| = B * q * v * sin θ where θ is the angle between velocity and magnetic field.
The direction of the force is perpendicular to both the velocity and the magnetic field and can be determined by Fleming's left-hand rule.

The force acting on a current-carrying conductor of length (l) carrying current (I) in a uniform magnetic field (B) is given by: F = I (l × B)
The direction of the force is perpendicular to both the current and the magnetic field.

The total force experienced by a charged particle moving in both electric (E) and magnetic (B) fields is called the Lorentz force.
It is given by: F = q (E + v × B)

When a charged particle enters a uniform magnetic field perpendicularly, it moves in a circular path.
The radius of the path is given by: r = (m * v) / (B * q) where m is the mass of the particle, v is its speed, B is the magnetic field, and q is the charge.
The period of circular motion is given by: T = (2πm) / (B * q)
When the charged particle enters the magnetic field at an angle other than 90 degrees, it follows a helical path.
The radius of the helical path is given by: r = (m * v * sin θ) / (B * q)
The pitch of the helix is given by: pitch = T * v * cos θ = (2π * m * v * cos θ) / (B * q)

Cyclotron is a device used to accelerate positively charged particles.
It uses strong electromagnetic fields to repeatedly accelerate ions through a region of electric field.
The radius of the circular path followed by the ions is given by: r = (m * v) / (B * q).
The frequency of the cyclotron is given by: v = (B * q) / (2πm) where B is the magnetic field, q is the charge of the particle, and m is the mass of the particle.
The maximum kinetic energy gained by the particle is: Emax = (B^2 * q^2 * r^2) / (2m) where ro is the maximum radius of the circular path.
Limitations include: not being able to accelerate uncharged particles and reaching a limit on the speed of heavier ions due to their relativistic mass increase.

The force between two infinitely long parallel current-carrying conductors is attractive if the currents are flowing in the same direction and repulsive if they flow in opposite directions.
The force per unit length is given by: F/l = (μo * I1 * I2) / (2πd) where I1 and I2 are the currents in the conductors and d is the distance between them.

The torque acting on a current-carrying coil placed in a uniform magnetic field is given by: τ = N * B * I * A * sin θ where N is the number of turns in the coil, B is the magnetic field intensity, I is the current, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the plane of the coil.

A moving coil galvanometer is a sensitive device used to detect and measure small electric currents.
It relies on the principle that a current-carrying coil placed in a magnetic field experiences a torque.
The deflection of the coil is proportional to the current flowing through it.
In equilibrium, the deflecting torque equals the restoring torque.

The current sensitivity of a galvanometer is the deflection produced per unit current and is given by: Is = θ/I = (N * B * A) / K where K is the restoring torque per unit twist.

The voltage sensitivity of a galvanometer is the deflection produced per unit voltage applied across it and is given by: Vs = θ/V = (N * B * A) / (K * R) where R is the resistance of the galvanometer.

An ammeter is a low resistance galvanometer that measures the current in a circuit.
It is connected in series with the circuit element being measured.

A galvanometer can be converted into an ammeter by connecting a low resistance (shunt S) in parallel to it.
The value of the shunt is calculated using the formula: S = (Ig * G) / (I - Ig) where Ig is the full-scale deflection current of the galvanometer, G is the resistance of the galvanometer, and I is the desired range of the ammeter - The ideal resistance of an ammeter is zero.