## F.Sc ICS Notes: Physics XII: Chapter 15 Electromagnetic Induction Numerical Problems

__An EMF of 0.45V is induced between the ends of a metal bar moving through a magnetic field of 0.22T. What field strength would be needed on EMF of 1.5 V bet. The ends of the bar, assuming that all other factors remain the same?__

**Numerical Problem 15.1:**__The flux density B in a region between the pole faces of a horse shoe magnet 0.5 wb/m(2) directed vertically downwards. Find the EMF induced in a straight wire 5cm long, perpendicular to B when it is moved in a direction at an angle of 60degree with the horizontal with a speed of 100cm/s.__

**Numerical Problem 15.2:**__A coil of wire has 10 loop. Each loop has an area of 1.5 * 10 (-3)m(2). A magnetic field perpendicular to the surface of each loop at all times. If the magnetic field is charged from 0.05T to 0.06T in 0.1 sec. Find the average EMF induced in the coil during this time.__

**Numerical Problem 15.3:**__A circular coil has 15 turns of radius 2cm each. The plane of the coil is inclined at 40 degree to a uniform magnetic field of 0.2T. If the field is increased to 0.5T in 0.2 sec, find the magnitude of the induced EMF.__

**Numerical Problem 15.4:**__Two coils are placed side by side. An EMF of 0.8V is observed in one coil when the current is changing at the rate of 200 A/s in the other coil. What is the mutual inductance of the coils?__

**Numerical Problem 15.5:**__A pair of adjacent coils has a mutual inductance of 0.1H. If the current in the primary changes from 0 to 10 A in 0.25s, what is the average induced EMF in the secondary? What is the change in flux in it if the secondary has 500 turns?__

**Numerical Problem 15.6:**__A solenoid has 250 turns and its self inductance is 2.4 mH. What is the flux through each turn when the current is 2A? What is the induced EMF when the current changes at 20 A/s?__

**Numerical Problem 15.7:**__A solenoid of length 8cm and cross sectional area 0.5cm(2) turns. Find the self inductance of the solenoid when the core is air. If the current in the solenoid increases through 1.5A in 0.2 sec, find the magnitude of induced EMF in it.__

**Numerical Problem 15.8:**__When current through a cell changes from 100 mA to 200 mA in 0.005 sec, an induced EMF of 40 mV is produced in the coil.__

**Numerical Problem 15.9:**(a) What is the self inductance of the coil?

(b) Find the increase in the energy stored in the coil.

__Like any field, the Earth's magnetic field stores energy. Find the magnetic energy stored in a space where strength of earth's field is 7 * 10(-5) T, if the space occupies an area of 10 * 10(8)m(2) and has a height of 750m.__

**Numerical Problem 15.10:**__A square coil of side 16cm has 200 turns and rotates in uniform magnetic field of magnitude 0.05 T. If the peak EMF is 12 V, what is the angular velocity of the cell?__

**Numerical Problem 15.11:**__A generator has a rectangular coil consisting of 360 turns. The coil rotates at 420 rev per min in 0.14 T magnetic field. The peak value of EMF produced by the generator is 50 V. If the coil is 5 cm wide, find the length of the side of the coil.__

**Numerical Problem 15.12:**__It is desired to make an A.C generator that can produce an EMF of 5kV with 50Hz frequency. A coil of area 1m(2) consisting of 200 turns is used as armature. What should be the magnitude of the magnetic field in which the coil rotates?__

**Numerical Problem 15.13:**__The back EMF in a motor is 120 V when the motor is turning at 1680 rev/min. What is the back EMF when the motor turns at 3360 rev/min?__

**Numerical Problem 15.14:**__A D.C motor operates at 240V and has a resistance of 0.5 ohm. When the motor is running at normal speed, the armature is 15A. Find the back EMF in the armature.__

**Numerical Problem 15.15:**__A copper ring has radius of 4cm and resistance of 1 milli ohm. A magnetic field applied over the ring, perpendicular to its plane. If the magnetic field increases from 0.2 T to 0.4 T in a time interval of 5 * 10(-3)s. What is the current in the ring during?__

**Numerical Problem 15.16:**__A coil of 10 turns and 35 cm(2) area is in a perpendicular magnetic field of 0.5T. The coil is pulled out of the field in 1s. Find the induced EMF in the coil as it is pulled out of the field.__

**Numerical Problem 15.17:**__An ideal step down transformer is connected to main supply of 240V. It is desired to operate a 12V, 30W lamp. Find the current in the primary and the transformation ratio?__

**Numerical Problem 15.18:**
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