No. 4.] MAGNETIC ATTRACTIVE FORCE. 2 3 3

ATTRACTIVE FORCE AND MAGNETIC INDUCTION.

BY GEO. E. POUCHER.

T T has been shown that for a magnet and its keeper the follow-J- ing formula holds :1

A SB2

A = ~sF where A is the attractive force in dynes, B the magnetic induction, and vS the area of the end of the bar in square centimeters. The experiment described in this paper is an attempt to test this law for objects not in immediate contact with the magnet.

Fig. 1.

Following the method of Ewing (Magnetic Induction in Iron and Other Metals) B was determined from the formulae B = 471/+ H and

0 < 2 2 ^ t a n 0

• MRW}' 1 Kapp, Dynamos, Alternators, and Transformers, pp. 51-68.

234 G. E. POUCHER. [VOL. XV.

Where OQ and OQ! are distances from the magnetometer needle to

the ends of the magnet ; a is the axis of the core of the magne t ;

Fx is the value of H at the point considered. In this case Fx =

0.138. Since H may be neglected in comparison with / w e have

All other terms being constants we wish to discover if A oc tan2 #.

.MICROM MICROSCOPE

Fig. 2.

The apparatus, as seen in the Figs. 1 and 2, consisted of an

electromagnet which had for a core a cylindrical soft-iron bar

2.6 x 67.0 cm. surrounded by a brass tube around which was

wound the solenoid of two layers of wire, each of 6.5 turns to the

centimeter. Above this was supported a copper bar 50.0 x 1.27 x

0.21 cm., from which was suspended a soft-iron sphere 4 cm. in

diameter, directly over the magnet. The deflections of this bar

were measured by a micrometer microscope focused on a black silk

fiber stretched over the center of one side. A magnetometer was

placed 158 cm. and afterwards at 135 cm. from the magnet, and its

deflections were read by use of a telescope and scale.

No. 4.] MAGNETIC ATTRACTIVE EORCE. 2 3 5

The experiment consisted simply in reading the deflection of the magnetometer needle, and the approach of the sphere to the magnet when a current was sent through the coils. The tables and plots are self-explanatory. In making the latter allowance was made for the fact that as the sphere approached the magnet the attraction increased according to the law of inverse squares. This was neces­sarily rough as the magnet's action was complex.

TABLE I. TABLE II.

Amperes.

.71

.98 1.27 1.62 1.96 2.41 2.65 3.05 3.30 3.61 4.01 4.48 5.13

Magneto­meter Scale

Reading.

4.6 6.5 8.7

11.4 14.0 17.3 19.1 21.6 23.6 25.3 26.8 28.3 30.1

Tan2 0

.000289

.000576

.001037

.001781

.002694

.004121

.005027

.006432

.007691

.009044

.009960

.011025

.012544

Micr. Reading.

.32

.64 1.01 1.51 2.11 3.21 4.01 5.16 6.07 7.16 8.09 9.13

10.49

Amperes.

.75 j 1.02

1.42 1.99 2.34 2.84 3.05 3.61 3.98 4.43 5.08

Magneto­meter Scale

Reading.

5.7 7.8

11.3 16.3 18.5 22.3 23.7 27.1 28.9 30.8 32.9

Tan£ 8

.000445

.000835

.001756

.003721

.004720

.006872

.007762

.010201

.011664

.013225

.015129

Micr. Reading.

.21

.50

.95 1.95 2.81 4.23 5.05 6.87 7.85 9.06

10.26

At the conclusion of each reading the micrometer was tested for the zero point, and it was found that errors due to residual magnet­ism or the instability of the apparatus were negligible.

Ld /* MICF

O,

OMETER

AT7RA

DIVISION?

CTICN

i. 1MM.= I

= 28.263 I

tf

/^*

DIV.

/ - ^O ^ 0

I

0 1.0 2.0 3.0 4.0 5.0 6.0 7-0 8.0 9.0 10.0

Fig. 3.

236 G. E. POUCHER. [ V O L . XV.

Fig. 4.

The exact relation between the induction and the attractive force expressed in Kapp's formula does not hold for objects at a distance from the magnet; but so far as these observations go they bear a constant relation to each other.

T H E PHYSICAL LABORATORY,

UNIVERSITY OF M A I N E .