Magnetic Field 27. B = B0 1 x Kˆ l f1 = force on AB = iB0[1 + 0]l = iB0l f2 = force on CD = iB0[1 + 0]l = iB0l f3 = force on AD = iB0[1 + 0/1]l = iB0l f4 = force on AB = iB0[1 + 1/1]l = 2iB0l Net horizontal force = F1 – F2 = 0 Net vertical force = F4 – F3 = iB0l 28. (a) Velocity of electron = Magnetic force on electron F = eB (b) F = qE; F = eB or, qE = eB eE = eB or, E = B dV V = (c) E = dr l V = lE = lB 29. (a) i = V0nAe i V0 = nae iBl iB (b) F = ilB = = (upwards) nA nA (c) Let the electric field be E iB iB E= Ee = An Aen dv (d) = E dV = Edr dr iB d = E×d = Aen –8 30. q = 2.0 × 10 C B = 0.10 T –10 –13 m = 2.0 × 10 g = 2 × 10 g 3 = 2.0 × 10 m/ R=
D l
B A
2m 2 3.14 2 10 13 –4 = = 6.28 × 10 s 8 1 qB 2 10 10 mv 31. r = qB T=
mv …(1) e0.1 4m V …(2) r= 2e 0.1 (2) ÷ (1) r 4mVe 0.1 4 = = = 2 r = 0.02 m = 2 cm. 0.01 2e 0.1 mv 2 –17 32. KE = 100ev = 1.6 × 10 J –31 2 –17 (1/2) × 9.1 × 10 × V = 1.6 × 10 J 0.01 =
2
1.6 10 17 2 9.1 10 31
= 0.35 × 10
14
34.5
l
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m 2 10 13 2 10 3 = = 0.2 m = 20 cm qB 2 10 8 10 1
V =
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