Practice Problems -Test 4

1.(a) The magnetic field inside a 24 cm diameter solenoid is increasing at therate if 2.4 T/s. How many turns should a coil wrapped around the outside of the solenoid have in order that the emf induced in the coil be 20 V?(b) An airplane with wingspan of 44m is in level flight at 300 m/s over the north pole, where the Earth's magnetic field has magnitude 0.62x10E-4 T and point vertically downward. Find the induced emf between the wing tips.

2.A square conducting loop 25 cm on a side lies at right angles to a uniform magnetic field. The loops resistance is 9.0 Ohms, and it carries a currentof 15 mA.  (i) At what rate is the magnetic field changing? (ii) How fast the same loop move in a region containing a uniform 1.2 T magnetic field?(iii) What is the direction of induced current in the loop?    (iv) How much is power dissipated in the loop?            X X X X X 

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3.(a) A rectangular conducting loop lies next to a long, straight wire carryinga current in the direction shown. In which direction is the induced current in the loop when the current in the wire is (i) increasing and (ii) decreasing. (Hint: use Lenz's law)(b) Find the magnetic flux through a circular loop 5 cm in diameter oriented with the loop at  60 deg. to a uniform 80 mT magnetic field.

4. (a) A long solenoid of cross-sectional are A and length l has n turns per unitlength. What is its self-inductance?(b) The current in an inductor is changing at the rate of 120 A/s, and the inductor emf is 40V. What is its self-inductance?

5. (a) A 5 turn coil is wrapped around a 10 cm long solenoid with cross-sectionalare 26 cm2, wound with 350 turns. Find the mutual inductance of this arrangement.(b) The current in a series RL circuit rises to half its final value in 8 s. What is the time constant?

6. A circular wire loop 40 cm in diameter has 100-ohm resistance and lies in a horizontal plane. A uniform magnetic field points vertically downward, and in 25 ms it increases linearly from 5.0 mT to 55 mT. Find the magnetic flux through the loop at (a) the beginning and (b) the end of the 25ms period.What is the loop current during this time? (d) Which way does this current flow?

7. A conducting loop of area 240 cm2 and resistance 12 Ohms lies at right angles to a spatially uniform magnetic field. The loop carries an induced current of 320 mA. At what rate is the magnetic field changing?

8.In Fig. 31-48 the 10 Ohm resistor is being moved to the right at a constant 50 cm/s. The 5 Ohm resistor, initially at rest, is placed across the conducting rails. Describe qualitatively its subsequent motion, and determine its final speed.

9. A circular loop 40 cm in diameter is made from a flexible conductor and lies at right angles to a uniform 12-T magnetic field.  At time t=0 the loop starts to expand, its radius increasing at the rate of 5.0 mm/s. Find the induced emf in the loop (a) at t=1.0s and (b) at t=10 s

10. Ch31 #43 Figure 31-52 shows a magnetic field pointing into the page; the field is confined to a layer of thickness  h in the vertical direction but extends infinitely to the left and right. The field strength is increasing with time: B= bt, where b is a constant. Find an expression for the electricfield at all points outside the region. Hint: Consult example 30-5.

11. Ch31 #46 A circular region of radius R lies in the x-y plane and contains a magnetic field given by B=Bo (r/R) k, where r is the radial distance from the central axis of the field region. Find an expression for the magnetic flux through this region.

12. Ch32 Ex 32-1 A 2-turn coil is wrapped around a long solenoid with cross-sectionalarea A = 26 cm2, wound with n=3500 turns per meter of length (Fig.32-2). Find the mutual inductance of this arrangement.

13.Ch32 #16 The current in a 2.0-H inductor is given by I = 3t^3 + 15t  +8, where t is in seconds and I is in amperes. Find an expression for the magnitude of the  inductor emf.

14.Ch32 #18 The current in a 40 mH inductor is given by I=Io e-bt, where I_o = 10 A and b=20/s.  What is the magnitude of the inductor emf at (a) t=0  (b) t=25 ms,  and  (c)t=50 ms?

15.Ch32 #29 In figure 32-7a, take R= 2.5  k Ohms and Eo=50V. When the switch isclosed, the current through the inductor rises to 10mA in 30 micro-seconds.(a) What is the inductance? (b) What will be the current in the circuit after many time constants?

16. Ch32 #46 A 500-turn solenoid is 23 cm long, 1.5 cm in diameter, and carries 65 mA. How much magnetic energy does it contain?

17. Two coils have a mutual inductance 580 mH.  One coil is supplied with a currentgiven by I= 3t2 - 2t + 4. What is the induced emf in the other coil at time t= 2.5 s?

18. What is the self-inductance of a solenoid 50m  long and .04m in diameter thatcontains 1000 turns of wire.