**UNSOLVED EXAMPLES**

**MAGNETISM**

**1.**The total flux of an electromagnet is 8 × 10^{-4}Wb.*(i)*If the cross-sectional area of the core is 100 mm^{2}find the flux density in the core.*(ii)*The electromagnet has 50 turns and a current of 2 flows thoughthe coil: If the length of the magnetic circuit is 200 mm, find the m.m.f. and magnetic field strength.

[Ans. (i) 8 T, (ii) 100 AT (iii) 500 At/m]

**2.**A long straight conductor carries a steady current of 10 A. Find*(i)*the intensity of magnetic field produced at a point 150 mm from the axis of the conductor and*(ii)*flux density of the field at that point.

[Ans. (i)10.61 A/m, 133.3 × 10^{-7 }T]

**3.**A Solenoid of 400 turns is wound on a continuous ring of magnetic material of relative permeability 1200. If the flux density of the magnetic material of the core in the solenoid is 1.3 T, what is the current in the solenoid? Mean diameter of the solenoid is 200 nm.

[Ans. 1.35A]

**4.**Two wires carrying current, in the same direction, of 5000 A and 10000 A are placed with their axis 50 mm apart. Calculate the force between them in N/m.

[Ans. 200 N/m]

**5.**Two long parallel linear conductors carry 50 A. If the conductors are separated by 25 mm find the force per meter length on the conductor if the current flow is (i) in the opposite direction*(ii)*in the same

[Ans. (i) 0.02 N (repulsive) (ii) 0.02 (alternative)]

**6.**An air cored toroidal coil has 3000 turns and carries a .current of 0.1 A. The length of the magnetic circuit is 150 mm and the cross-sectional area of the coil is 400 mm^{2}, Calculate: (i) Magnetic field strength (ii) flux density and*(iii)*total flux within the coil.

[Ans, (i) 2000 AT/m, (ii) 2.51 × 10^{-3} T, (iii) 1.004 × 10^{-6} Wb]

**7.**A cast steel ring of 200 mm mean diameter and 300 mm^{2}cross-section has a winding of 200 turns. If the relative permeability of steel is 1000, what current will be required produce a flux of 3.75 × 10^{-4}Wb.

[Ans. 3.17 A]

**8.**An iron ring of mean length 500 mm has an air gap of 1 mm and a winding of 200 turns. If the permeability of is 400 when a current of 1.25 A flows through the coil, find the flux density.

[Ans, 0.134 T]

**9.**An iron ring of 100 mm mean diameter is made of15 mm round iron of permeability 900, has an air gap 5 mm wide. It has 400 turns. If the current through this winding is 3.4 A, determine:*(i)*magnetomotive force, (ii) the total reluctance of the circuit,*(iii)*the flux in the ring and*(iv)*the flux density in the ring.

[Ans. (i) 1360 AT, (ii) 0.2394 × 10^{8} AT/Wb, (iii) 5680 × 10^{-8} Wb, (iv) 0.321T]

**10.**A magnetic ring has a mean circumference of 1.5 m and is of 0.01 m2 in cross-section, and is wound with 175 turns. A saw cut of 4 mm width is made in the ring. Calculate the magnetising current required to produce a flux of 0.8 m Wb in the air gap.

Assume leakage factor as 1.25 and permeability of iron as 400.

[Ans. 3.16 A]

**ELECTROMAGNETISM**

**11.**A flux of 4 × 10^{-4}Wb is created by a current of 10 A flowing through a 100 turn coil. Calculate the inductance of coil corresponding to a complete reversal of the current in 0.01 second. Find the magnitude of induced e.m.f.

[Ans. 4 × 10^{-3} H ; 8 V]

**12.**The field winding of a D.C. electromagnet is wound with 960 turns and has resistance of 50 Ω when exciting voltage is 230 V, the magnetic flux linking with the coil is 0.005 Wb. Calculate:*(i)*The self-inductance of the coil*(ii)*The energy stored in the magnetic field.

[Ans. (i) 1.0435 H ; (ii) 11.04 J]

**13.**A solenoid has 1200 turns and carries a current of 2 A. The iron core has a length of 0.4 m and cross- section of 80 cm^{2}, the relative permeability is 1,000. Calculate the self-induced e.m.f. in the solenoid, if the current is switched off in 0.01 second.

[Ans. 7238 V]

**14.**A coil of 300 turns, wound on a core of non-magnetic material has an inductance of 10 mH. Calculate:

*(i) *The flux produced by A current of5 A;

*(ii) *The average value of e.m.f. induced when a current of 5 A is reversed in 8 milli seconds.

[Ans. (i) 0.1667 m Wb, (ii) 12.5 V]

**15.**Two coils A and B are wound on the same iron core. There are 500 turns on A and 3,000 turns on B. A current of 5 amperes through coil A produces a flux of 600 × 10^{6}Wb in the core. If this current is reversed in 0.02 s, calculate the average e.m.f. induced in coils A and B.

[Ans. 30 V; 180 V]

**16.**Two coils A of 12500 turns and B of 16000 turns, lie in parallel planes so that 60% of the flux produced in A links coil B. It is found that a current of 5 A in A produces a flux of 0.6 × 10^{-3}Wb while. the same current in B produces 0.8 × 10^{-3}Wb, Determine:

*(i) *Mutual inductance ;

*(ii) *Coefficient of coupling.

[Ans. (i) 1.15 H; (ii) 0.5861]

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