Magnetic induction – problems and solutions

1. The following factors influence the magnetic induction on the conductor wire.

(1) the current flowing in the wire

(2) permittivity

(3) wire density

(4) the distance of a point from the wire

Which statements are correct

Solution :

The equation of magnetic induction of a wire :

μ_{o }= Permeability of a vacuum or magnetic constant

I = Electric current flowing on the wire

r = the distance of a point from the wire

B = the magnitude of magnetic induction

2. Note the statements related to the following magnetic induction.

(1) the current flowing in the wire

(2) the permeability of a vacuum

(3) wire cross-sectional area

(4) wire density

What affects magnetic induction magnitudes on a wire conductor.

Solution

Learn the magnetic induction formula and previous description.

3. The electric current I flows on the conductor wire. What is the magnetic induction at the center of the circle (P)? (µ_{o} = 4π.10^{-7} Wb.m^{-1}.A^{-1})

__Known :__

Radius of circle (r) = 6 cm = 6 x 10^{-2} meters

Electric current (I) = 8 Ampere

Permeability of a vacuum (µ_{o}) = 4π x 10^{-7 }Wb.A^{-1} m^{-1}

__Wanted:__ the magnetic induction at the center of the circle (P)

__Solution :__

360^{o} – 90^{o} = 270^{o}. 270^{o} / 360^{o} = 3/4 then 270^{o} = 3/4 circumference

The magnetic field formula at the center of the coil with a number of loops:

*B = magnetic field, N = number of windings, I = electric current, r = radius of curvature*

In the above problem, there is only one winding so that N is removed from the equation. The wire coil on the above problem is not 1 circle but 3/4 circle. The above formula is adjusted again with this problem :

The magnetic induction at the center of the circle :

4. Current 2 A flows on a circular wire like the picture. What is the magnitude and direction of magnetic induction at point P if the radius of circle 4π cm.

__Known :__

Radius (r) = 4π cm = 4π x 10^{-2} meters

Electric current (I) = 2 Ampere

Permeability of a vacuum (µ_{o}) = 4π x 10^{-7 }Wb.A^{-1} m^{-1}

__Wanted :__ The magnitude and direction of magnetic induction at point P

__Solution :__

The wire coil on the above problem is 1/2 circle.

The magnitude of magnetic induction at point P :

20 conceptual questions and answers related to magnetic induction:

**1. Question:** What is magnetic induction?

**Answer:** Magnetic induction, or magnetic flux density, is a measure of the concentration of magnetic field lines in a given area. It’s represented by the symbol B and has units of Tesla (T).

**2. Question:** How is magnetic induction related to the magnetic field?

**Answer:** Magnetic induction is the quantitative representation of a magnetic field, indicating its strength and direction at any given point in space.

**3. Question:** What is Faraday’s law of electromagnetic induction?

**Answer:** Faraday’s law states that the electromotive force (EMF) induced in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit.

**4. Question:** How does the orientation of a coil affect the magnetic induction experienced by it?

**Answer:** The magnetic induction experienced by a coil is maximum when the plane of the coil is perpendicular to the magnetic field and minimum when the plane is parallel.

**5. Question:** What role does magnetic induction play in transformers?

**Answer:** In transformers, alternating magnetic induction in the primary coil induces an EMF in the secondary coil, allowing for the transfer of electrical energy between coils.

**6. Question:** How does the motion of a conductor in a magnetic field lead to electromagnetic induction?

**Answer:** When a conductor moves in a magnetic field, the number of magnetic field lines passing through it changes, leading to an induced EMF according to Faraday’s law.

**7. Question:** What is the unit of magnetic induction?

**Answer:** The unit of magnetic induction is the Tesla (T), equivalent to Weber per square meter (Wb/m²).

**8. Question:** How is Lenz’s law related to magnetic induction?

**Answer:** Lenz’s law states the direction of the induced EMF and current resulting from electromagnetic induction. It opposes the change in magnetic flux that produced it.

**9. Question:** Why is iron often used as a core in induction coils?

**Answer:** Iron is ferromagnetic and can easily be magnetized. When used as a core, it enhances the magnetic induction and concentrates the magnetic field lines, increasing the coil’s efficiency.

**10. Question:** How is the magnitude of the induced EMF affected by the rate of change of magnetic flux?

**Answer:** The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux.

**11. Question:** What is mutual induction?

**Answer:** Mutual induction refers to the process where a change in the current of one coil induces an EMF in a nearby coil due to the changing magnetic field.

**12. Question:** How can the efficiency of electromagnetic induction be increased in a system?

**Answer:** Efficiency can be increased by using materials with high magnetic permeability, reducing resistive losses, and optimizing the coil’s design and orientation relative to the magnetic field.

**13. Question:** What is self-induction?

**Answer:** Self-induction occurs when a changing current in a coil induces an EMF in the same coil due to its changing magnetic field.

**14. Question:** How does the number of turns in a coil affect magnetic induction?

**Answer:** Increasing the number of turns in a coil amplifies the induced EMF, given a constant rate of change of magnetic flux.

**15. Question:** What role does magnetic induction play in electric generators?

**Answer:** In electric generators, mechanical motion (often rotational) causes a change in magnetic flux in coils, leading to electromagnetic induction and the generation of alternating current (AC).

**16. Question:** Can magnetic induction occur with static magnets and stationary conductors?

**Answer:** No, for magnetic induction to occur, there needs to be a relative motion between the magnet and the conductor, or the magnetic field itself must be changing.

**17. Question:** How is magnetic induction related to magnetic permeability?

**Answer:** Magnetic permeability measures a material’s ability to support the formation of a magnetic field. Materials with higher magnetic permeability can concentrate magnetic field lines, leading to greater magnetic induction.

**18. Question:** What happens to the induced EMF when a conductor moves faster through a magnetic field?

**Answer:** The induced EMF increases with the speed of the conductor moving through the magnetic field, given a constant magnetic field strength.

**19. Question:** Can two coils with different cross-sectional areas have the same magnetic induction?

**Answer:** Yes, magnetic induction (B) is independent of the coil’s cross-sectional area but depends on the magnetic field strength and the coil’s orientation relative to the field.

**20. Question:** How does the phenomenon of electromagnetic induction support the principle of energy conservation?

**Answer:** Electromagnetic induction transforms mechanical energy (motion) into electrical energy (and vice versa). While the form of energy changes, the total energy remains conserved.

Understanding magnetic induction and its principles enables advancements in various technologies, from power generation to electronic devices.