Magnetic Field

The protons, cathode rays and the alpha particles are charged particles, so these are deflected by the magnetic field. But neutrons have not any charge, so these are not deflected by magnetic field.

Concept: Physics (Atoms) – Magnetic Field produced by Bohr's Orbiting Electron.

Step 1: Identify proportionalities for radius and angular velocity. In Bohr's model for the orbit:
• Radius
• Angular velocity

Step 2: Relate current to angular velocity. The equivalent current due to the orbiting electron is . Therefore, .

Step 3: Determine the magnetic field proportionality. The magnetic field at the center of a circular current loop is . $ $

Concept: Physics (Magnetism) - Magnetic Field of a Current Loop and Ohm's Law.

Step 1: Relate the currents through the magnetic field. The magnetic field at the center is . Given and : $ R l = 2\pi r V = IR $

Step 1: Magnetic field inside solenoid. Field inside long solenoid: $ N=10 I=0.4 r=0.1 \pi^2=10 $

Concept: Physics (Magnetic Effects of Electric Current) - Magnetic Moment of a Current Loop.

Step 1: State the formula for magnetic moment. The magnetic moment of a current-carrying loop is the product of the current and the area enclosed by the loop. $ L R L $

Let magnetic field at is and at is

or
Or
or

Step 1: Cyclotron frequency relation.
The cyclotron frequency is given by:

Step 2: Expression for magnetic field.

Step 3: Kinetic energy of accelerated proton.
Radius of circular path:

Step 4: Kinetic energy expression.

Step 5: Conclusion.
The correct pair is .

The magnetic field at a point along the axis of a current-carrying loop is given by the formula: Where: - (permeability of free space), - (current), - (radius of the loop), - (distance from the center along the axis). Substituting the values: Simplifying: Thus, the magnetic field is .

Concept: Magnetic induction, also known as magnetic flux density, represents the strength of a magnetic field at a particular point. It is denoted by .

Step 1: Definition of magnetic induction. Magnetic induction describes the number of magnetic field lines passing through a unit area perpendicular to the magnetic field.

Step 2: SI unit. The SI unit of magnetic induction is Tesla (T).

Step 3: Conclusion. Thus, the SI unit of magnetic induction is Tesla (T).

Concept: Magnetic induction, also known as magnetic flux density, is a measure of the strength and direction of a magnetic field at a given point in space. It is usually represented by the symbol . Magnetic induction describes how strongly a magnetic field acts on moving electric charges, current-carrying conductors, or magnetic materials. It plays a fundamental role in electromagnetism and appears in many important laws such as the Lorentz force law and Faraday’s law of electromagnetic induction. The SI unit of magnetic induction is the Tesla (T). One tesla is defined as the magnetic flux density that produces a force of one newton on a one-meter conductor carrying a current of one ampere placed perpendicular to the magnetic field. Magnetic induction is also related to magnetic flux by the relation: where = magnetic flux (measured in Weber) = area perpendicular to the magnetic field Thus, another equivalent unit form is:

Step 1: Understanding magnetic induction.
Magnetic induction represents the intensity of the magnetic field acting over a unit area.

Step 2: Identifying the SI unit.
The SI unit used to measure magnetic flux density is Tesla (T).

Step 3: Using the unit relationship.
From the relation , Hence, the SI unit of magnetic induction is Tesla (T).

Concept: When a charged particle moves perpendicular to a magnetic field, it experiences a magnetic force providing the centripetal force. Rearranging, where = mass of electron , = charge of electron .

Step 1: Substitute the given values.

Step 2: Simplify the expression. Thus, the radius of the circular path is approximately m.

Step 1: Understanding the Concept:
Magnetic induction, also known as magnetic flux density or magnetic field , represents the strength of a magnetic field.
It defines the force experienced by a moving charge or a current-carrying wire in the field.

Step 2: Key Formula or Approach:
The approach is to identify the standard International System of Units (SI) for various electromagnetic quantities.
We will evaluate each option against standard physical definitions.

Step 3: Detailed Explanation:
Let us analyze each given option systematically.
Option (A) is Weber (Wb), which is the SI unit for magnetic flux ( ).
Option (B) is Tesla (T), which is the internationally accepted SI unit for magnetic induction or magnetic flux density.
Option (C) is Henry (H), which is the SI unit for electrical inductance ( ).
Option (D) is Gauss (G), which is indeed a unit of magnetic induction, but it belongs to the older CGS system, not the SI system.
Therefore, Tesla is the only correct SI unit among the choices.

Step 4: Final Answer:
The SI unit of Magnetic Induction is Tesla.

Concept: Magnetic induction, also known as magnetic flux density, represents the strength and direction of the magnetic field at a given point. It is denoted by . The SI unit of magnetic induction is Tesla (T). One Tesla is defined as the magnetic field that exerts a force of one Newton on a charge of one Coulomb moving with a velocity of one meter per second perpendicular to the magnetic field. Mathematically, where = magnetic induction, = magnetic force, = charge, = velocity of charge, = angle between velocity and magnetic field.

Step 1: Understanding Tesla. Thus, Tesla is also equivalent to Weber per square meter.

Step 2: Comparison with other units.
• Weber (Wb) is the unit of magnetic flux.
• Henry (H) is the unit of inductance.
• Gauss is the CGS unit of magnetic field. Therefore, the SI unit of magnetic induction is Tesla.

Concept: Magnetic Induction (also called Magnetic Flux Density) is represented by . It measures the strength of a magnetic field over a given area. It is defined as magnetic flux per unit area: where
• = Magnetic induction
• = Magnetic flux
• = Area perpendicular to the field The SI unit of magnetic flux is Weber (Wb). Therefore, This unit is called the Tesla (T).

Step 1: Use the definition of magnetic induction.

Step 2: Substitute SI units.

Step 3: Identify the named SI unit. Thus the SI unit of magnetic induction is