What is (self) inductance L? Put a definition or describe meaning or effect You

Question

What is (self) inductance L? Put a definition or describe meaning or effect You buy a "superconducting magnet", a 20 cm long solenoid made from NbTi wire (that becomes a superconductor with R=0 when cooled down to4K) with N=10,000 turns around a diameter of 10 cm. Estimate the inductance L for this (ideal) solenoid. How large should be the magnetic field B inside the solenoid when a current l=100A runs through it? (assume always long ideal solenoid) To ramp the current up to l=100A you need a power supply that can provide high currents. What limits the ramping speed? How long does is take to increase steadily the current from 0 to 100A without exceeding a higher voltage than 4V? Neglect for this estimate the actual small resistance R in the circuit due the external leads. When l=100A is reached, the current remains steady flowing through L, the resistance R=0.01 Ohm and power supply. What is now the voltage V_0 the power supply has to deliver and what is V_L across L and V_R across R?

Explanation / Answer

{a}ans

the phenomenon of inducing emf in a coil due to flow of current which changes with time in the same coil

{b} ans

length L=20 cm =20*10^-2 m

number of turns N=10000

diameter d=10 cm

radius r=5 cm

area A=3.14*25*10^-4 =78.5*10^-4 m

therefore the self inductance of a solenoid

L=4*3.14*10^-7[N]^2 A/l

=4*3.14.10^-7*10^8*78.5*10^-4/20*10^-2

=49.29*10^-1

=4.93 H

[c]

the magnetic field inside the solinoid

B=4*3.14*10^-7*10000*100

=12.56*10^-1

=1.26 T

[d]

e.m.f=4v

current changes di=100 A

basing on co.efficient of self inductance

E=L di/dt

4=4.93*100/dt

dt=4.93*100/4

=123.25 sec

[e]

current i=100 A

resistance R=0.01 ohms

volatage across the resistance Vr= iR=100*0.01

=1 v

now we assuming current I= E/Z

where Z= impedence

Z=E/i = 4/100 =0.04

but Z= [ R^2 + (Xl)^2]^1/2

Xl=[Z^2 -- R^2]^1/2

=[0.04^2 --0.01^2]^1/2

=[16-1]^1/2 *10^-2

=3.873*10^-2

therefore the inductance of voltage Vl= I(xl)

=100*10^-2*3.873

=3.873 v

so the volatage Vo =[Vr^2+Vl^2]^1/2

=[1+(3.873)^2]^1/2

=4 V

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