All questions of Magnetostatics for Electrical Engineering (EE) Exam

Given data:
L1 = 0.5 H (inductance of coil 1)
L2 = 4.0 H (inductance of coil 2)
k = 0.8 (coefficient of coupling)
i1 = 20 sin 314t A (current through coil 1)

To find:
Maximum value of the induced EMF in coil 2.

Formula:
The mutual inductance (M) between two coils is given by:
M = k * sqrt(L1 * L2)

The induced EMF in the second coil is given by:
e2 = -M * di1/dt

where di1/dt is the rate of change of current through coil 1.

Calculation:
Using the formula for mutual inductance, we can calculate the value of M as follows:
M = k * sqrt(L1 * L2)
= 0.8 * sqrt(0.5 * 4.0)
= 0.8 * sqrt(2.0)
≈ 0.8 * 1.414
≈ 1.131 H

Since the current through coil 1 is given by i1 = 20 sin 314t A, we can calculate the rate of change of current as follows:
di1/dt = d/dt (20 sin 314t)
= 20 * d/dt (sin 314t)
= 20 * 314 * cos 314t A/s

The maximum value of cos 314t is 1, so we can substitute this value to calculate the maximum rate of change of current:
di1/dt = 20 * 314 * 1
= 6280 A/s

Finally, we can calculate the maximum value of the induced EMF in coil 2 using the formula:
e2 = -M * di1/dt
= -1.131 * 6280 V
≈ -7091.48 V

The negative sign indicates that the induced EMF in coil 2 is in the opposite direction to the change in current in coil 1.

Since the maximum value of the induced EMF is given as a positive value, we take the absolute value:
|e2| ≈ 7091.48 V

Therefore, the maximum value of the induced EMF in coil 2 is approximately 7.1 kV (kilovolts). Hence, the correct answer is option C.

The force on a conductor is given by F = BIL sin θ, where B = 3.75, I = 8, L = 0.12 and θ = 300. We get F = 3.75 x 8 x 0.12 sin 30 = 1.8 units.

Answer:

In order to understand the answer to this question, it is important to have a basic understanding of magnetic lines of force and the unit of magnetic flux, which is the Maxwell.

Magnetic Lines of Force:
Magnetic lines of force, also known as magnetic field lines, are imaginary lines used to represent the direction and strength of a magnetic field. These lines are used to visualize and describe the magnetic field around a magnet or a current-carrying conductor.

The Maxwell:
The Maxwell is a unit of magnetic flux, which measures the amount of magnetic field passing through a given area. It is equivalent to one magnetic line of force.

Conversion:
Given that 100 Maxwells is the quantity to be converted, we need to determine how many magnetic lines of force are equivalent to 100 Maxwells.

Since 1 Maxwell is equivalent to one magnetic line of force, 100 Maxwells would be equal to 100 magnetic lines of force.

Therefore, the correct answer is option 'B', which states that 100 Maxwells is equal to 100 magnetic lines of force.

The force due to a current element is given by F = BI x L. Thus F = 12 x 5 x 0.02 = 1.2 units.

Maxwell's law is an important law in electromagnetism that relates the magnetic field and its sources. It is derived from Ampere's law, which describes the magnetic field generated by a current-carrying wire. Maxwell's law is given by:

Curl(H) = J

Explanation:

Curl(H) is the curl of the magnetic field H. It describes how the magnetic field changes in space. J is the current density, which describes the amount of current flowing through a given area. The equation states that the curl of the magnetic field is equal to the current density, which means that the magnetic field is generated by the current flowing through a wire.

Maxwell's law is important because it relates the magnetic field and its sources. It is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields. The other three equations are Gauss's law, Gauss's law for magnetism, and Faraday's law of induction. Together, these four equations form the foundation of electromagnetism and are used to describe a wide range of phenomena, from the behavior of electric motors to the propagation of electromagnetic waves.

Conclusion:

In conclusion, Maxwell's law is derived from Ampere's law and relates the magnetic field and its sources. It is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields. The equation states that the curl of the magnetic field is equal to the current density, which means that the magnetic field is generated by the current flowing through a wire.

Explanation:

Electric field and magnetic field are two fundamental concepts in electromagnetism. In the case of a conductor, the distribution of electric and magnetic fields is unique.

Electric Field:
- The electric field is maximum outside the conductor. This is because the charges on the surface of the conductor redistribute themselves in such a way that the electric field inside the conductor is zero.
- This phenomenon is known as electrostatic shielding, where the charges rearrange themselves to cancel out the external electric field inside the conductor.

Magnetic Field:
- In contrast to the electric field, the magnetic field is maximum inside the conductor. When a current flows through a conductor, a magnetic field is generated around it according to Ampere's law.
- Inside the conductor, the magnetic field lines are concentrated due to the flow of current. This results in a higher magnetic field strength inside the conductor compared to outside.

Conclusion:
- Therefore, it is true that the electric field is maximum outside the conductor, while the magnetic field is maximum inside the conductor. This distinction is essential in understanding the behavior of electromagnetic fields around conductors.