626
13 Electromagnetism I
ξ = vl B
∴
v =
ξ
l B
=
2
0.2 × 1.0
= 10 m/s
13.74 ξ = −
dφ
dt
= −
AdB
dt
A = area of the triangle sandwiched between the ends of the rod and the
radii connecting the centre with the ends, Fig. 13.18:
A =
1
2
(base)(altitude) =
1
2
l
R 2 − (l/2) 2
Thus
ξ = −
dB
dt
l
2
R 2 − (l/2) 2
13.75 Gravitational force on the loop
F g = mg sin θ
Magnetic force on the loop
F m = (B cos θ) il = B cos θ
ξ l
R
=
B cos θ l
R
v B cos θ · l =
v B 2 l 2 cos 2 θ
R
For steady speed, F net = F m − F g = 0
∴
v B 2 l 2 cos 2 θ
R
− mg sin θ = 0
or
v =
mg R sin θ
B 2 l 2 cos 2 θ
13.76 ξ = π R 2 B f
∴
B =
ξ
π R 2 f
=
6.28 × 10 −3
3.14 × (0.1) 2 (1200/60)
= 0.01 T
13.77
[emf] = [electric field][distance]
= [force/charge][distance]
= [MLT
−2 Q
−1
][L] = [M L
2 T
−2 Q
−1
]
[dφ B /dt] = [φ B ][T
−1
] = [B][area][T
−1
]
= [force/(velocity) charge][L
2
][T
−1
]
= [MLT
−2
/LT
−1 Q][L
2
][T
−1
]