Compute the magnetic field inside the solenoid.

+4 votes

37.0 mA current is carried by a uniformly wound air-core solenoid with 425 turns, a 17.0 mm diameter, and 11.5 cm length.

(a) Compute the magnetic field inside the solenoid. 
  µT

(b) Compute the magnetic flux through each turn. 
  T·m2

(c) Compute the inductance of the solenoid. 
  mH 
(d) Which of these quantities depends on the current? (Select all that apply.)
 

 

asked Mar 6, 2012 in Physics by Joey33 ~Expert~ (1,216 points)
edited Mar 11, 2012 by Joey33
    
the answer for part B is 9.181e-8 and i think is wrong why?????????

1 Answer

+2 votes
 
Best answer

Part A:

The magnetic field within a solenoid is given by the formula

magnetic field = permeability of free space * (N/L) * I  (*where N=number of turns, L=length, I=current)

permeability of free space = 4pi * 10^-7 T*m/A

I = 37 mA = 37*10^-3 A

N =425 turns

L = 11.5 cm = 11.5*10^-2 m

plugging into the formula for magnetic field we get

magnetic field = (4pi * 10^-7 T*m/A) * (425 / 11.5*10^-2 m) * (37*10^-3 A)

magnetic field  = 1.72*10^-4 T = 172  µT

Part B:

Magnetic flux can be found by muliplying the magnetic field by the Area of the solenoid.

Area = pi*r^2

where r = (17/2) mm = (17/2)*10^-3 m

Area = pi*((17/2)*10^-3 m)^2

Magnetic flux = Magnetic field * Area

Magnetic flux = (1.72*10^-4 T )*  pi*((17/2)*10^-3 m)^2

However since we are finding the magnetic flux through each turn we need to divide the answer by the total number of turns:

Magnetic flux through each turn= ((1.72*10^-4 T )*  pi*((17/2)*10^-3 m)^2 ) / 425

Magnetic flux  through each turn= 3.9*10^-8 T*m^2

 

Part C:

There are several ways to find the inductance.

The easiest way, since we already know the magnetic flux and the current, we can find inductance through the following formula:

Inductance = total magnetic flux / current

*we would need to multiply the magnetic flux through each turn by total number of turns to get back the total magnetic flux

Inductance  = 425*(3.9*10^-8 T*m^2)* (37*10^-3 A)

answered Mar 11, 2012 by kirby ~Expert~ (3,020 points)
edited Apr 24, 2012 by kirby
The calculation for inductance is wrong
the answer for part B is 9.181e-8 and i think is wrong why????????
part C answer should be 425*(3.9*10^-8 T*m^2)/(37*10^-3 A)
symbolically it is (N*B)/I

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