z. A toroid has a square cross section as shown in Fig.( r ) with the length ofan edge equal to the radius of the inner surface. The ratio of themagnitude of the magnetic field at the inner surface to the magnitude'ofthe field at the outer surface is:(a) % (b) % (c) t ((t) 2 (e) 4

3. A conducting bar moves near a long wire carrying a constant 50-Acurrent as shown in Fig.(l). lf a:4.0 mm, Z:50 cm, and v: l2m/s, what is the potential difference, Vo- Vr?

Assignment 10

Choose the correct answer.

l. Two long ideal solenoids (with radii 20mm and 30 mm, respectively) have the same number of turnsof wire per unit length. The smaller solenoid is mounted inside the larger, along a common axis. Themagnetic field within the inner solenoid is zero. The current in the inner solenold must be:(a) two-thirds the current in the outer solenoicl(b) one-third the current in the outer solenoid(c) twice the cunent in the outer solenoicl(d) half the current in the outer solenoid(e) the same as the current in the outer solenoid

. .' ,.., ..,..,,..i

*-----+&iri

Fig. t

(a) +15 mV(d) -20 mV

(b) -15 mV (c) +20 mV(e) +10 mV A -10 mV

4. A rectangular coil with resistance R has Nturns, each oflength / and width w as shown in Figure (2). The coil movesinto a uniform magnetic field B with constant velocity valong the x axis. The width of the magnetic field region is3w.

(i) Magnetic flux through the looparea as a function of position isgiven by

Fig.(1)

F*,r---Il*******ll"******llxxxxxxrll^****^*llxxxxxrxl

Fig.2

t-t'l__l r

(ii) Induced emf through theloop area as a function ofposition is given by

(iii) Total magnetic force on theloop area as a function of positionis given by

r, 2\, 3r' ltt'

_i_ _--LJ@

5. Abar (L: 80 cm) moves on two frictionless rails, as shown,in Fig. (6) a region where the magnetic field is uniform (B :0.30 T) and into the paper. If v: 50 cm/s and R = 60 mO,what is the magnetic force on the moving bar?@) 0.a8 N tu the right(c) 0.32 N to the teft(e) None of the above

(b) 48 N to the left(d) 0.32 N to the right

Fig.(6)

7. A long solenoid (radius: 3.0 cm, 2500 turns per meter) caries a current given by /= 0.30 sin(200 r)A, where I is measured in s. When t:2.5 ms, what is the magnitude of th-e induced electric fieid at apoint which is 4.0 cm from the axis of the solenoid?

(c) 6.7 x t0-3 V/m

1. A square wire loop with 2 m sides is perpendicular to a magnetic field, withhalf the area of the loop in the field as shown in the Fig.18. The loopcontains a20Y battery with negligible internal resistance. If the magnitudeof the field varies with time according to 8:0.042 - 0.87t, where B ii Testaand r in seconds. What are (a) the net emf in the circuit and (b) the directionof the current in the circuit (clockwise or anticlockwise)?

2. A long solenoid has 400 turns per meter, 6 cm radius and carriesa current 1 = 30(r - ,- r'611A. outside the solenoid and coaxial *d.with it is acoilthathas aradius R= 7 cm and consists of atotal I '

turns N:250 of fine wire as shown in Fig.(10). What are (a) theinduced emf in the coil and (b) the direction of the current in thecoil (clockwise or anticlockwise)? [po = 4nx ] 0'? S.l.U.]

----) 3. A.rectangular loop of width a, length & and number of turns 1/ is fixed near a long"/ wire carrying current lwhere I : I"(l-e-d). The distance between the wire andclosest side of the loop is c as shown in Fig.l1. Find (a) the emf in the loop at /:1/(3a) second, (b) the direction of the induced current in the loop (clockwise oranticlockwise) and (c) the magnetic force on the loop after a very long time?

(a) 9.3 x I0-3 V/m

(d) 5.3 x I0-3 V/m

Problems

(b) 5.0 * t0-3 u/m

(e)1.9 xt0-3 V/m

Fig. 9 66;1 ,1a111-1

_/ N turns

\l^mtJJiJ J J l

I '1i. Ili' Fig.l o

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