6.A solenoid of radius 1.50 cm has 600 turns and a length of 15.0 cm. (a) Find i
ID: 1522650 • Letter: 6
Question
6.A solenoid of radius 1.50 cm has 600 turns and a length of 15.0 cm.
(a) Find its inductance. ______mH
(b) Find the rate at which current must change through it to produce an emf of 90.0 mV. (Enter the magnitude.) ______A/s
7.The current in a 60.0-mH inductor changes with time as i = 4.00t2 5.00t, where i is in amperes and t is in seconds. (a) Find the magnitude of the induced emf at t = 1.00 s. _______mV
(b) Find the magnitude of the induced emf at t = 4.00 s. _______mV
(c) At what time is the emf zero? __________s
Explanation / Answer
6)
a)
Given:-
N = 600,
r = 0.015 m,
d = 0.15 m,
o = 4 x 10^-7 H/m
The inductance of a solenoid is given by:
L = oN^2A/d
L = oN^2(r^2) / d
L = (4 x 10^-7) x 600^2 x 3.14 x 0.015^2 / 0.15
L = 2.1297 mH
b)
emf = L (delta I /delta t)
90 x 10^-3 = 2.1297 x 10^-3 ( delta I /delta t)
delta I / delta t = 42.26 A/s
7)
V(t) = L(dI/dt)
V(t) = (60 x 10^-3 H)(8t - 5 s)
a)
V(1) = (60 x 10^-3 H)(8 - 5 s)
V(1) = - 0.180 V
(b)
V(4) = (60 x 10^-3 H)(4*8 - 5 s)
V(4) = 1.62 V
(c)
0 = (60 x 10^-3 H)(8t - 5 s)
0 = 8t - 5
t = 0.625 s
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