## Electromagnetism solved Problems

### Magnetic circuit with an air gap

1. An iron ring has its mean length of flux path as 60 cm and its cross-sectional area as 15 cm². If relative permeability is 500. Find the current required to be passed through a coil of 300 turns wound uniformly around it to produce a flux density of 1.2 T. What would be the flux density with the same current if the iron ring is replaced by an air core.
2. A magnetic circuit has a mean length of flux path of 20 cm and a cross-sectional area of 1 cm² relative permeability of its material is 2400. Find the MMF required to produce a flux density of 2 T in it. If an air gap of 1 mm is introduced in it. Find the MMF required for the air gap as a fraction of the total MMF to maintain the same flux density.
3. A ring-shaped core is made up of two parts of the same material. Part one is a magnetic path of length 25 cm and with a cross-sectional area of 4 cm², whereas part two is of length 10 cm and cross-sectional area of 6 cm². The flux density in part two is 1.5 T. If the current through the coil, wound over core is 0.5 A. Calculate the number of turns of the coil. Assume µ = 1000 for material.
4. A ring has a diameter of 21 cm and a cross-sectional area of 10 cm². The ring is made up of semi-circular sections of cast iron and cast steel with each joint having reluctance equal to an air gap of 0.2 mm. Find the ampere-turns required to produce a flux of 8 X 10⁻⁴ Wb. The relative permeabilities of cast steel and cast iron are 800 and 166 respectively.
5. A metallic ring of a uniform cross section of 2 cm² and a mean diameter of 20 cm is wound with 1000 turns of wire. When the coil carries a current of 1 A. The flux in the ring is 240 µWb. Calculate –
1. Relative permeability of the material.
2. The magnetic Field strength in the ring.
6. An iron ring has a mean circumference of 180 cm. It carries a current of 1.5 A and has 600 turns of coil wound over it. The relative permeability of iron is 1200. Calculate –
1. MMF
2. Field strength
3. Flux density.
7. A shunt field coil is required to develop 1500 AT with an applied voltage of 60 V. The rectangular coil has a mean length of turn of 50 cm. Calculate the wire size resistivity of copper is 2 X 10⁻⁶ Ωcm at the operating temperature of the coil. Estimate the number of turns if the coil is to be worked at a current density of 3 A/mm².

### Self Inductance

1. The mean diameter of a steel ring is 40 cm and flux density of 0.9 Wb/m² is produced by 3500 AT/m. If the cross section of the ring is 15 cm² and the number of turns is 440. Calculate –
1. The exciting current.
2. The self-inductance.
3. Exciting current and inductance when air gap of  cm is cut in the ring
2. An air-cored circular coil has 500 turns and a mean diameter of 20 cm and a cross-sectional area of 5 cm². Find –
1. Inductance.
2. The average value of EMF induced in the coil if a current of 4 A is reversed in 0.1 sec.
3.  An iron core choke is designed to have an inductance of 20 H when operating at a flux density of 1 T; the corresponding relative permeability of the iron core is 2000. Determine the number of turns in the winding of the choke given that the flux path has a mean length of 22 cm in the iron core and 1 mm in the air gap and that its cross-section is 10 cm².
4. The mean diameter of a steel ring is 50 cm and a flux density of 1 T is produced in it by magnetic field strength of 40 A/cm. If the cross section of the ring is 20 cm² and the cross section of the ring is 20 cm² and the number of turns 500, find –
1. Inductance.
2. Exciting current and the inductance when a gap 10 mm long is cut in the ring the flux density being maintained at 1 T. Neglect leakage and fringing.

### Mutual Inductance

1. Two identical coils P and Q each with 1500 turns are placed in parallel planes near to each other so that 70% of the flux produced by the current in coil P links with coil Q. If a current of 4 A is passed through any one coil if produces a flux of 0.04 mWb linking with itself. Find the self-inductance of the two coils, The mutual inductance, and the coefficient of coupling between them.
2. Two coils A and B in a magnetic circuit have 600 and 500 turns respectively. A current of  8 A in coil A produces a flux of 0.04 Wb. If the coefficient of coupling is 0.2. Calculate –
1. Self Inductance of coil A when coil B is open-circuited.
2. Flux linkage with coil B
3. Mutual inductance
4. EMF induced in B when flux changes from zero to full value in 0.02 sec.
3. A coil of 100 turns have a mean diameter of 5 cm is placed coaxially at the center of a solenoid 50 cm long wound with 2500 turns and carrying a current of 3 A. Determine the inductance of the arrangement.
4. Two coils X and Y, X of 1200 turns and Y of 1500 turns lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5 A in X produces 0.05 mWb while the same current in Y produces 0.075 mWb. Calculate mutual inductance.

### Energy stored in magnetic field

1. An air core coil 1.5m long, 8 cm diameter has 5000 turns. Calculate –
1. Magnetic field strength.
2. Inductance.
3. Energy stored in the field, when the current 12 A passes through it.
2. An air-core solenoid 1 m in length and 10 cm in diameter has 5000 turns. Calculate –
1. Self-inductance.
2. Energy stored in the magnetic field when the current of 2 A flows in a solenoid.
3. An iron ring of 10 cm in diameter and 8 cm² in cross section is wound with 300 turns of wire. For a flux density of 1.2 Wb/m² and µr = 500. Find the exciting current, the inductance, and the energy stored.
4. A magnetic core is in the form of a closed ring of mean length 20 cm and cross-sectional area 1 cm². Its µr is 2400. A coil of 2000 turns is uniformly wound around it. Find the flux density set up in the core if a current of 66 mA is passed through the coil. Find the inductance of the coil if an air gap of 1 mm is cut in the ring perpendicular to the direction of flux.
5. A coil is wound on an iron ring core to form a solenoid a certain current is passed through the coil which is producing a flux of 40 µWb. The length of the magnetic circuit is 75 cm while its cross-sectional area is 3 cm². Calculate the energy stored in the circuit if µr = 1500.

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