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Pre-lab EM-9 The magnetic field of a solenoid The magnetic field along the axis of a solenoid can be viewed as generated by many single current loops. The total field can be calculated by integrating the field generated by all of the single current loops. The axial component of the field as a function of distance x from the midpoint of a solenoid can be expressed as Honl B = L+2x L-2x (1) 2 D2 +(L+2x) D +(L-2x)) where L is the length, Dis the diameter of the solenoid, n is the number of turns per unit length on the solenoid, and7 is the current in the solenoid. At the midpoint of the solenoid, x 0, the magnetic field is Be = Honl- (2) VD2 +L2 If the solenoid is long and thin, L>>D, then B = He nl is true for most points inside the solenoid. If the solenoid is short, and L and D are comparable, then the magnetic field inside the solenoid would vary with position. B po nl is true only for the points at or near the center of the solenoid. Immediately outside the wall of the solenoid, the magnetic field is zero. The magnetic field at and near the openings of the solenoid varies with position. Given the diameter of the solenoid D 1.0 cm, length L-20 cm, n=4000 turn/m, and I=1.0 A, use Eq. (1) to calculate the magnetic field at the following positions: Be = D=1.0 cm, L= 20 cm D+(L+2x) (cm') D+(L-2x) (cm) x(cm) (L +2x) (cm) (L-.2x) (cm) B (mT) 7. 10 Sample calculation of B (x) for x= Scm

Pre-lab EM-9 The magnetic field of a solenoid The magnetic field along the axis of a solenoid can be viewed as generated by many single current loops. The total field can be calculated by integrating the field generated by all of the single current loops. The axial component of the field as a function of distance x from the midpoint of a solenoid can be expressed as Honl B = L+2x L-2x (1) 2 D2 +(L+2x) D +(L-2x)) where L is the length, Dis the diameter of the solenoid, n is the number of turns per unit length on the solenoid, and7 is the current in the solenoid. At the midpoint of the solenoid, x 0, the magnetic field is Be = Honl- (2) VD2 +L2 If the solenoid is long and thin, L>>D, then B = He nl is true for most points inside the solenoid. If the solenoid is short, and L and D are comparable, then the magnetic field inside the solenoid would vary with position. B po nl is true only for the points at or near the center of the solenoid. Immediately outside the wall of the solenoid, the magnetic field is zero. The magnetic field at and near the openings of the solenoid varies with position. Given the diameter of the solenoid D 1.0 cm, length L-20 cm, n=4000 turn/m, and I=1.0 A, use Eq. (1) to calculate the magnetic field at the following positions: Be = D=1.0 cm, L= 20 cm D+(L+2x) (cm') D+(L-2x) (cm) x(cm) (L +2x) (cm) (L-.2x) (cm) B (mT) 7. 10 Sample calculation of B (x) for x= Scm

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Pre-lab EM-9 The magnetic field of a solenoid The magnetic field along the axis of a solenoid can be viewed as generated by many single current loops. The total field can be calculated by integrating the field generated by all of the single current loops. The axial component of the field as a function of distancex from the midpoint of a solenoid can be expressed as Honl B 3= L+2x L-2x (1) 2 /D2 + (L+2x)2 D2 + (L-2x)2) where L is the length, D is the diameter of the solenoid, n is the number of turns per unit length on the solenoid, and7 is the current in the solenoid. At the midpoint of the solenoid, x 0, the magnetic field is Be = Honl (2) VD2 +12 If the solenoid is long and thin, L>>D, then B = 4, nl is true for most points inside the solenoid. If the solenoid is short, and L and D are comparable, then the magnetic field inside the solenoid would position. B= po nl is true only for the points at or near the center of the solenoid. ary with Immediately outside the wall of the solenoid, the magnetic field is zero. The magnetic field at and near the openings of the solenoid varies with position. Given the diameter of the solenoid D 1.0 cm, length L-20 cm, n=4000 turn/m, and I= 1.0 A, use Eq. (1) to calculate the magnetic field at the following positions: Be =ラ4onl: D=1.0 cm, L= 20 cm D+(L+2x) (cm) D+(L-2x) (cm) x(cm) (L +2x) (cm) (L-2x) (cm) B (mT) 7. 10 Sample calculátion of B (x)for x Scm
Transcribed Image Text:Pre-lab EM-9 The magnetic field of a solenoid The magnetic field along the axis of a solenoid can be viewed as generated by many single current loops. The total field can be calculated by integrating the field generated by all of the single current loops. The axial component of the field as a function of distancex from the midpoint of a solenoid can be expressed as Honl B 3= L+2x L-2x (1) 2 /D2 + (L+2x)2 D2 + (L-2x)2) where L is the length, D is the diameter of the solenoid, n is the number of turns per unit length on the solenoid, and7 is the current in the solenoid. At the midpoint of the solenoid, x 0, the magnetic field is Be = Honl (2) VD2 +12 If the solenoid is long and thin, L>>D, then B = 4, nl is true for most points inside the solenoid. If the solenoid is short, and L and D are comparable, then the magnetic field inside the solenoid would position. B= po nl is true only for the points at or near the center of the solenoid. ary with Immediately outside the wall of the solenoid, the magnetic field is zero. The magnetic field at and near the openings of the solenoid varies with position. Given the diameter of the solenoid D 1.0 cm, length L-20 cm, n=4000 turn/m, and I= 1.0 A, use Eq. (1) to calculate the magnetic field at the following positions: Be =ラ4onl: D=1.0 cm, L= 20 cm D+(L+2x) (cm) D+(L-2x) (cm) x(cm) (L +2x) (cm) (L-2x) (cm) B (mT) 7. 10 Sample calculátion of B (x)for x Scm
Since x is measured from the midpoint of the solenoid, x increases toward the opening of the solenoid. The value of B at x 0 is the field strength at the midpoint of the solenoid, and the value of B at x 10 cm is the field strength at the opening of the solenoid. B decreases as x increases. How fast does the field strength decrease with x at various points? If the diameter of the solertoid D is 5.0 cm, the length of the solenoid is 20 cm, n 4000 turns/m, and / 1.0A, again calculate the magnetic fields at different positions. D 5.0 cm, L 20 cm D+(L+2x) (cm) D+(L-2x (cm) x(cm) (++2x) (cm) (L-2x) (cm) B (mT) 10 How fast does the magnetic field decrease with x compare with the previous case? Now use B =H, nl to calculate the magnetic field. How does this field value compare to the values you calculated using the dimensions of the solenoid? Is it close to the value at the mid-point of the solenoid or at the opening of the solenoid?
Transcribed Image Text:Since x is measured from the midpoint of the solenoid, x increases toward the opening of the solenoid. The value of B at x 0 is the field strength at the midpoint of the solenoid, and the value of B at x 10 cm is the field strength at the opening of the solenoid. B decreases as x increases. How fast does the field strength decrease with x at various points? If the diameter of the solertoid D is 5.0 cm, the length of the solenoid is 20 cm, n 4000 turns/m, and / 1.0A, again calculate the magnetic fields at different positions. D 5.0 cm, L 20 cm D+(L+2x) (cm) D+(L-2x (cm) x(cm) (++2x) (cm) (L-2x) (cm) B (mT) 10 How fast does the magnetic field decrease with x compare with the previous case? Now use B =H, nl to calculate the magnetic field. How does this field value compare to the values you calculated using the dimensions of the solenoid? Is it close to the value at the mid-point of the solenoid or at the opening of the solenoid?
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