Magnetic Field MCQ Quiz - Objective Question with Answer for Magnetic Field - Download Free PDF

Explanation:

Motor:

• A motor converts electrical energy into mechanical energy.
• The principles of the motor are based on electromagnetism. A current-carrying conductor produces a magnetic field around it and a current-carrying conductor is placed perpendicular to the magnetic field so that it experiences a force.
• A motor can run off of direct current and alternating current.
• The direction will be given by Fleming's left-hand rule.

Generator:

• A generator converts mechanical energy to electrical energy.
• It works on the principle of electromagnetic induction.
• The phenomenon of electromagnetic induction is the production of induced current in a coil placed in the region where the magnetic field changes with time. The magnetic field may change due to relative motion between the coil and a magnet placed near the coil. If the coil is placed near a current-carrying conductor, the magnetic field may change either due to a change in the current through the conductor or due to the relative motion between the coil and conductor.
• The direction of the induced current is given by Fleming's right-hand rule.

Electric bells:

• Electric wells work on the magnetic effect of electric current.
• An electric bell consists of an electromagnet, striker, and gong. 
• When the circuit is closed, the electromagnet attracts the striker towards it. The striker hits the gong and produces a sound.

Electric Heater:

• An electric heater is a device that transforms a current of electricity into heat.

 Thus, from the above discussion, we can say that Electric Heater does not involve the principle of ‘magnetic effect of electric current’ in its working.

Calculation:

Each arc subtends an angle α = π/4 at the center. The magnetic field at the center due to a current-carrying arc of radius r that subtends angle α is given by:

B = (μ₀ × i × α) / (4πr)

Since there are four arcs of each radius and the current in each arc contributes a field in the same direction (out of the paper), the net magnetic field is the sum of the fields due to all arcs:

B₁ = 4 × (μ₀ × i × α) / (4πr₁) + 4 × (μ₀ × i × α) / (4πr₂)

Factoring out common terms:

B = (μ₀ × i × α) / 4 × [1 / r₁ + 1 / r₂]

Now, substituting the values:

μ₀ = 4π × 10⁻⁷ T·m/A, i = 10 A, α = π/4, r₁ = 0.08 m, r₂ = 0.12 m

B = (4π × 10⁻⁷ × 10) / 4 × [1 / 0.08 + 1 / 0.12]

B = 6.54 × 10⁻⁵ T

Answer: 6.54 

CONCEPT:

The magnetic field at a distance d for a finite conducting wire carrying a current I 

B = \(\frac{ \mu_0 I}{4\pi d} (\sin θ_1 + \sin θ_2)\) ----(1)

(where θ1 and θ2 are the angles made with the endpoints of the wire)

EXPLANATION:

The inner angle of the hexagon = 360°/6 = 60°

⇒ ∠BOD = 60°

Now, we divide ∠BOD into equal parts such that ΔOBD divide into two right-angled triangles 

So, ∠BOX = ∠DOX = 30°

For the right-angled triangles ΔBOX and ΔDOX

one angle is 90°, one angle is 30°

∴ The remaining angle will be 180° - (90+30)° = 60°

∴ ∠OBX = ∠ODX = 60°

Now, in ΔOBX 

sin 60° = OX/OB = OX/R

⇒OX = R sin 60° = R√3/2

So, the magnetic field B = \(\frac{ \mu_0 I}{4\pi d} (\sin θ_1 + \sin θ_2)\)

B = \( \frac{ \mu_0 I}{4\pi (\frac{R\sqrt{3}}{2})} (\sin 30°+\sin30°) = \frac{ \mu_0 I}{2\sqrt{3}\pi R}\)

For 6 sides the net magnetic field = 6B = 6×\( \frac{ \mu_0 I}{2\sqrt{3}\pi R}\) = \(\frac{\sqrt{3} \mu_0 I}{\pi \mathrm{R}}\)

Hence the correct answer is option 4.

Ans.(2)

Sol.

Wavelength of photon emitted \(\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{\mathrm{n}_{2}^{2}}-\frac{1}{\mathrm{n}_{1}^{2}}\right)(\because \mathrm{Z}= 1)\) Transaction from second orbit to first orbit : We have, n₁ = 2n₂ = 1

∴ \(\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{1^{2}}-\frac{1}{2^{2}}\right) \Rightarrow \mathrm{R}=\frac{4}{3^{\lambda}}\)

Transaction from third orbit to first orbit:

A current-carrying wire generates a magnetic field as a result of the moving charges inside the conductor. A current-carrying conductor is a neutral species under electromagnetism's rules until an external charge or electric field is added to it.

Calulation:
The given problem involves a current flowing through the segments ABC and A'B'C'. The goal is to calculate the magnetic field at point P. Using Ampère's law, we can calculate the magnetic field created by each segment and then find the total field at P.

The magnetic field due to the segment AB is:

B₁ = (μ₀I / 4πr) [sin θ₁ + sin θ₂], where θ₁ = 0° and θ₂ = 90°.

Thus, B₁ = (μ₀I / 4πr) [0 + 1] = μ₀I / 4πr (Into the paper)

The magnetic field due to the segment A'B' is calculated in a similar way:

B₂ = (μ₀I / 4πr) [sin θ'₁ + sin θ'₂], where θ'₁ = 0° and θ'₂ = 90°.

Thus, B₂ = (μ₀I / 4πr) [0 + 1] = μ₀I / 4πr (Into the paper)

The total magnetic field at point P, Bₚ, is the sum of B₁ and B₂:

Bₚ = B₁ + B₂ = μ₀I / 4πr + μ₀I / 4πr = μ₀(2I) / 4πr

Hence, the magnetic field at P is 2μ₀I / 4πr (Option 2).

The correct answer is Both Poles.   

 Important Points

• The ancient Greeks were the first known to have used this mineral, which they called a magnet because of its ability to attract other pieces of the same material and also iron.
• Englishman William Gilbert was the first to investigate the phenomenon of magnetism systematically using scientific methods.
• The closer the lines, the stronger the magnetic field, so in bar magnet, the magnetic field closest to the poles. 
• It is equally stronger at both the poles, the force in the middle of the magnet is weaker and halfway between the poles and the centre.
• The magnetic field is a vector quantity that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
• A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to that of the magnetic field.
• S.I unit of the magnetic field is Tesla.

Electric field: An electric field is a physical region that surrounds each electric charge and exerts a force on all other charges in the region, either by attraction or repulsion.

Electric fields originate from electric charges, or from time-varying magnetic fields.

​Magnetic field: A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

Important Conclusions:

• A charge that is moving in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field.
• Moving charges will generate a magnetic field.
• Electric fields originate from electric charges, or from time-varying magnetic fields.
• Moving charges will generate a magnetic field.
• So a moving electrical charge produces an electric as well as a magnetic field. Hence, option 1 is correct.

CONCEPT:

• Magnetic field strength or magnetic field induction or flux density of the magnetic field is equal to the force experienced by a unit positive charge moving with unit velocity in a direction perpendicular to the magnetic field.
  • The SI unit of the magnetic field (B) is weber/meter2 (Wbm-2) or tesla.
• The CGS unit of B is gauss.

​1 gauss = 10-4 tesla.

EXPLANATION:

• From the above explanation, we can see that the relation between tesla and gauss is given by:

1 tesla = 104 gauss​. 

Explanation:

Magnetic field and magnetic lines of force: It is the space around a magnetic pole or magnet or current-carrying wire within which its magnetic effect can be experienced is defined as a magnetic field.

• The magnetic field can be represented with the help of a set of lines or curves called magnetic lines of force or magnetic field lines.

Properties of magnetic field line:

1. The magnetic field line is directed from the north pole to the south pole outside and south to the north inside the magnet.
2. Magnetic field lines are closed and continuous.
3. Magnetic field lines are more crowded near poles which shows that the strength of the magnetic field is maximum at its poles.
4. Magnetic field lines never intersect with each other.

​The reason being is that if two field lines intersect each other, then there will be two directions of the magnetic field, which is not possible.

The correct answer is parallel straight lines.

Key Points

• The magnetic field lines inside a solenoid are in the form of parallel straight lines. Hence, Option 4 is correct.
• This pattern of field lines inside the solenoid indicates that the strength of the magnetic field is the same at all points.
• When current passes through the wires, a magnetic field is produced.
• Solenoid behaves like a permanent bar magnet.
• Whose south and north poles are the ends from where magnetic field lines are coming in and out, respectively.

Important Points

• There are two types of solenoid: finite and infinite solenoid.
• A finite solenoid is the one whose length is finite and the infinite is the one whose length is infinite such that the end effects are negligible.
• The magnetic field lines are parallel to the axis of the long infinite solenoid and the magnetic field does not vary along the length.
• The magnetic field almost seems to be a straight line.
• A coil of many circular turns of insulated copper wire wrapped closely in a cylinder’s shape is called a solenoid.
• The field pattern is identical to that of a magnetic field around a bar magnet.
• The solenoid’s one end acts as a magnetic north pole, while the other acts as a magnetic south pole.
• Within the solenoid, the field lines are in the form of parallel straight lines.
• It means that the magnetic field within the solenoid is the same at all points.
• That is, the field within the solenoid is uniform.
•  

Concept:

Magnetic Effect of Current

A current-carrying conductor produces a magnetic field around us. 

The magnetic force depends upon the magnitude of current and distance from the conductor. 

This property of the current is used to make an electromagnet. 

Electromagnet

• An electromagnet is a temporary magnet that should ideally have the property to behave as a magnet when current passes through it and lose magnetism as soon as the current is stopped.
• Soft iron is generally used for making electromagnets because it has high magnetic permeability, i.e. it can easily gain magnetic properties when current is passed around the core and quickly lose when the current is stopped.
• The soft iron inside the coil makes the magnetic field stronger because it becomes a magnet itself when the current is flowing

Explanation:

• So, an electromagnet behaves as magnet when switch is ON and loses magnetisam when switch is  off. 
• This makes electromagnet a temporary magnet. 

So, the correct option is a temporary magnet.

CONCEPT:

Magnetic field lines:

• A magnetic field line is an imaginary line such that tangent to it at any point gives the direction of the magnetic field at that point in space.
• Magnetic field lines are drawn to represent the magnetic fields.
• Magnetic field lines can be drawn with the help of a magnetic compass.
• Magnetic field lines are also called magnetic lines of force.

Properties of magnetic field lines:

1. The magnetic field lines of a magnet (or a solenoid) form continuous closed loops.
2. The magnetic field lines start from the north pole and end on a south pole outside the magnet. Inside the magnet, the magnetic field lines start from the south pole and end on the north pole.
3. The tangent to the magnetic field line at a given point represents the direction of the net magnetic field B at that point.
4. The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
5. The magnetic field lines do not intersect with each other if they did, there will be two directions of the magnetic field at that point which is not possible.

EXPLANATION:

• The magnetic field lines start from the north pole and end on a south pole outside the magnet. Hence, option 2 is correct.
• Inside the magnet, the magnetic field lines start from the south pole and end on the north pole.

CONCEPT:

• Magnetic Field is a field in space around a magnet or moving charged particle where another magnet or moving charged particle experiences a Force.
  • A moving charged particle produces a magnetic field.
  • A current-carrying wire contains moving electrons into it, hence generate a magnetic field around it.
• Magnetic Field generated around the current (I) carrying conductor at a distance R from the wire:

\(\Rightarrow \vec B = \frac{\mu_0\vec I}{2\pi R}\)

Where \(\frac { \mu_0}{2\pi}\) has a constant value, I is current, and R is the distance of the point from the wire.

EXPLANATION:​

Magnetic field intensity, 

\(\Rightarrow B = \frac{μ_0I}{2π r}\) 

\(⇒ B ∝ \frac{1}{r}\)

• From the above formula, it is clear that the magnetic field generated is inversely proportional to the distance from the current-carrying wire.

Concept:

The field around a current-carrying wire or around a magnetic in which the magnetic force can be experienced by another current-carrying wire or by another magnet is called magnetic field.

The magnetic field at the centre of the circular coil is given by:

\(B = \frac{{{\mu _0}\;I}}{{2\;R}}\)

Where B = strength of magnetic field, I = current, R = radius of the circular coil

Calculation:

Length of the wire is L

⇒ L = 2π R

We know that the magnetic field at the centre of the wire is

\(B = \frac{{{\mu _0}\;I}}{{2\;R}} \Rightarrow I = \frac{{2BR}}{{{\mu _0}}}\)

Multiplying ‘π‘ both sides

\(I \times \pi = \frac{{2\;B\;R \times \pi }}{{{\mu _0}}} = \frac{{\left( {2\pi R} \right)B}}{{{\mu _0}}} = \frac{{L\;B}}{{{\mu _0}}}\)

\( \Rightarrow I = \frac{{L\;B}}{{{\mu _0}\pi }}\)

Hence, the current in the wire must be \(\frac{{B\;L}}{{{\mu _0}\pi }}\)

Concept:

Magnetic field:

• The space or region around the current-carrying wire/moving electric charge or around a magnet in which force of magnetism can be experienced by other magnetic material is called as magnetic field/magnetic induction by that material/current.
• It is denoted by B.

The magnetic force per unit length between two parallel wires is given by;

\(F = \frac{{{\mu _{0\;}}{I_1}\;{I_2}}}{{2\pi \;d}}\)

Where μ₀ is the permittivity of free space, I₁ is d.c current in the first wire and I₂ is d.c current in the second wire and d is the distance between two wires.

Explanation:

Given two wires carrying current Ia and Ib

The length of both wire is -

The force per unit length between the two wires is \(\frac{F}{L} \Rightarrow \;F=\frac{{{\mu _{0\;}}L\;{I_a}\; {I_b}}}{{2\pi \;d}}\)

Since the current goes in same direction So it is of attraction.

Important Points

• If the conductor carries current in the same direction, then the force between them will be attractive.
• If the conductor carries current in the opposite direction, then the force between them will be repulsive