Physics Chapter on Magnetic Fields

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Questions and Answers

What is the relationship between the kinetic energy of a proton and a deuteron when both have the same charge and potential?

The kinetic energies of the proton and deuteron are equal, represented by Kp:Kd = 1:1.

Using Fleming’s left hand rule, how do you determine the direction of magnetic force on a positively charged particle?

Adjust the thumb, forefinger, and middle finger such that forefinger points to the magnetic field and middle finger points to the velocity; the thumb then indicates the direction of the magnetic force.

If the radius of the circular path of a proton is 10 cm, what would be the radius of the path for the deuteron?

The radius of the circular path for the deuteron is also 10 cm.

What is the ratio of the periodic times of a proton and an alpha particle if the ratio of their masses and charges is applied in the periodic time formula?

<p>The ratio of the periodic times is Ta:Tp = 2:1.</p> Signup and view all the answers

Deduce the formula for the radius of a charged particle's circular path in a magnetic field.

<p>The radius is given by the formula $r = \sqrt{\frac{mv^2}{qB}}$.</p> Signup and view all the answers

How is the total resistance of an ammeter calculated when combining two resistances in parallel?

<p>The total resistance G' is calculated as $G' = \frac{GS}{G + S}$.</p> Signup and view all the answers

What kinetic energy comparison exists between an alpha particle and a proton?

<p>The kinetic energy of the alpha particle is twice that of the proton, Kp:Ka = 1:2.</p> Signup and view all the answers

What is the significance of the charge and mass ratio when determining the radius of circular paths of particles in a magnetic field?

<p>The charge and mass ratio influence the radius, as changes in these parameters will alter the radius according to $r = \sqrt{\frac{mK}{qB}}$.</p> Signup and view all the answers

Calculate the radius of the circular path of an electron with energy 45 eV in a magnetic field of intensity 9 x 10^5 Wb/m^2.

<p>The radius is 0.25 meters.</p> Signup and view all the answers

What does Fleming’s left-hand rule represent regarding the motion of charged particles?

<p>Fleming’s left-hand rule shows the direction of the magnetic force acting on a positively charged particle, with the thumb, forefinger, and middle finger representing different vectors.</p> Signup and view all the answers

For particles entering a magnetic field with the same energy, how do the kinetic energies of a proton, deuteron, and alpha particle compare?

<p>The kinetic energy ratio is Kp:Kd:Ka = 1:1:2.</p> Signup and view all the answers

If the radius of the circular path of a proton is 10 cm in a magnetic field, what would be the radii for a deuteron and an alpha particle?

<p>Both the deuteron and alpha particle have a radius of 14.14 cm.</p> Signup and view all the answers

How do you calculate the ratio of periodic time for a proton and an alpha particle in a magnetic field?

<p>The ratio is Ta:Tp = 2:1.</p> Signup and view all the answers

What is the expression used to find the radius of a charged particle moving in a magnetic field?

<p>The radius is expressed as r = (mv)/(qB).</p> Signup and view all the answers

Explain how the mass and kinetic energy of a charged particle affect its radius in a magnetic field.

<p>A heavier mass or higher kinetic energy increases the radius of the particle’s circular motion in the magnetic field.</p> Signup and view all the answers

Describe the factors that determine the direction of the force on a charged particle in a magnetic field according to Fleming’s left-hand rule.

<p>The direction of the magnetic field and the velocity of the particle determine the direction of the force.</p> Signup and view all the answers

What does Fleming's Left Hand Rule represent?

<p>Fleming's Left Hand Rule is used to determine the direction of motion of a conductor in a magnetic field, indicating the orientation of force, magnetic field, and current.</p> Signup and view all the answers

How do you calculate the magnetic force on a charged particle in a magnetic field?

<p>The magnetic force can be calculated using the formula $F = q(v \times B)$, where $q$ is the charge, $v$ is the velocity vector, and $B$ is the magnetic field vector.</p> Signup and view all the answers

Define a solenoid and its function.

<p>A solenoid is a coil of wire that generates a magnetic field when an electric current passes through it, commonly used to create a controlled magnetic field.</p> Signup and view all the answers

What is the significance of the angle of entry of a charged particle in a magnetic field?

<p>The angle impacts the radius of the helical path; for example, a 60° angle results in a specific radius based on the velocity and magnetic field strength.</p> Signup and view all the answers

Explain the nature of the path of a charged particle moving perpendicular to both electric and magnetic fields.

<p>The particle will follow a straight line trajectory in the presence of mutually perpendicular electric and magnetic fields.</p> Signup and view all the answers

Calculate the radius of the helical path for an electron in a 0.3 tesla magnetic field at an angle of 60° with a speed of $4 \times 10^5$ m/s.

<p>The radius $r$ is given by $r = (\sqrt{3}/2) \times 10^{-5}$ meters, calculated using the formula $r = mv/(Bqsinθ)$.</p> Signup and view all the answers

What happens to the magnetic force on a charged particle when the magnetic field and velocity are parallel?

<p>When the magnetic field and velocity are parallel, the magnetic force acting on the charged particle is zero.</p> Signup and view all the answers

What role does the number of turns in a solenoid play in its magnetic field strength?

<p>The magnetic field strength inside a solenoid is directly proportional to the number of turns per unit length and the current flowing through it.</p> Signup and view all the answers

Flashcards

Fleming's Left Hand Rule

A rule used to determine the direction of the force on a current-carrying conductor in a magnetic field.

Magnetic Force Equation

F = q(v x B), where F is force, q is charge, v is velocity, and B is magnetic field.

Solenoid

A coil of wire that produces a strong magnetic field when an electric current flows through it.

Magnetic field inside a solenoid

Magnetic field is uniform inside the solenoid

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Charged particle in perpendicular electric/magnetic field

Charged particle path will be helical.

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Helical path of electron

Path of an electron moving in a magnetic field at an angle.

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Radius of helical path (electron)

Radius of the helical path depends on the initial velocity, magnetic field, and charge.

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Pitch of helical path (electron)

Distance between successive turns in a helical path.

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Force on a charged particle in a magnetic field

The force experienced by a charged particle moving in a magnetic field is perpendicular to both the velocity of the particle and the magnetic field direction. This force is determined by the charge of the particle, its velocity, and the magnetic field strength.

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Radius of circular path in a magnetic field

The radius of the circular path followed by a charged particle moving in a uniform magnetic field is determined by the particle's mass, charge, velocity, and the magnetic field strength. It is directly proportional to the particle's momentum and inversely proportional to the magnetic field strength.

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Kinetic energy of a charged particle

The kinetic energy of a charged particle is the energy it possesses due to its motion. It is determined by the particle's mass and velocity. For a charged particle in an electric field, the kinetic energy is also proportional to the potential difference traversed.

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Ratio of kinetic energies of particles in a magnetic field

The ratio of kinetic energies of charged particles moving in a uniform magnetic field depends on their charge and mass. If they experience the same potential difference, the kinetic energy is proportional to the charge of the particle.

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Ratio of radii of circular paths in a magnetic field

The ratio of radii of circular paths followed by charged particles moving in a uniform magnetic field is directly proportional to the ratio of their momenta and inversely proportional to the ratio of their charges.

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Ratio of periodic times of particles in a magnetic field

The ratio of periodic times of charged particles moving in a uniform magnetic field is directly proportional to the ratio of their masses and inversely proportional to the ratio of their charges.

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Magnetic field at the center of a current-carrying coil

The magnetic field at the center of a current-carrying coil is directly proportional to the number of turns in the coil, the current flowing through it, and the permeability of the medium. It is inversely proportional to the radius of the coil.

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Radius of Circular Path of Charged Particle

The radius of the circular path followed by a charged particle moving in a magnetic field is given by r = (√2mK)/(eB), where r is the radius, m is mass, K is kinetic energy, e is charge, and B is magnetic field.

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Ratio of Kinetic Energies for Proton, Deuteron, and Alpha Particle

The ratio of kinetic energies of a proton, deuteron, and alpha particle moving in the same magnetic field is 1:1:2.

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Ratio of Radii for Proton, Deuteron, and Alpha Particle

The ratio of the radii of the circular paths followed by a proton, deuteron, and alpha particle moving in the same magnetic field is 1:√2:√2.

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Ratio of Periodic Times for Proton and Alpha Particle

The ratio of the periodic times of a proton and an alpha particle moving in the same magnetic field is 1:2.

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Ammeter Resistance

The resistance of an ammeter is G’ = (G * S) / (G + S) where G is the shunt resistance and S is the galvanometer resistance.

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Study Notes

Magnetic Fields and Charged Particles

  • A charged particle moving in a magnetic field will follow a straight path if the field and velocity are parallel. If perpendicular, a circular path results.
  • Fleming's left-hand rule dictates the direction of force on a moving charged particle in a magnetic field.
  • The magnitude of the force is calculated using the formula F = qvBsinθ, where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between v and B.

Solenoids

  • A solenoid is a coil of wire wound in a helical manner.
  • It produces a uniform magnetic field inside.
  • The magnitude of the magnetic field inside a solenoid is given by the formula B = μ₀nI, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.

Magnetic Field at the Center of a Current Loop

  • The magnetic field at the center of a circular current loop is given by the formula B = μ₀I/2R, where μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.

Magnetic Field on Axis of a Current Loop

  • The magnetic field at a point on the axis of a current loop is calculated using the formula B = (μ₀I R²)/2(R² + x²)^3/2, where μ₀ is the permeability of free space, I is the current, R is the radius of the loop, and x is the distance from the center of the loop to the point on the axis.

Path of a Charged Particle in Combined Fields

  • The path will be a helix if an electric and a magnetic field are both perpendicular to the direction of the velocity.

Specific Charge of an Electron

  • Specific charge (e/m) can be calculated using the formula e/m = 2y v2 / Ex2, where:
    • y = deflection in the y-direction
    • v = initial velocity of the electron
    • E = electric field strength
    • x = distance the electron moves in the x-direction.

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