Apparatus:

Gouy balance setup, paramagnetic sample, electromagnet, analytical balance, power supply.

Formula Used:

Magnetic susceptibility (χm) can be determined using the formula:

χm = (2 × Δm × g) / (μ₀ × H² × l)

Where:
  χm = Magnetic susceptibility
  Δm = Change in mass (mass reading with and without the sample)
  g = Acceleration due to gravity
  μ₀ = Permeability of free space (4π × 10⁻⁷ T·m/A)
  H = Magnetic field strength
  l = Length of the sample

Theory:

The Gouy balance method is based on the principle that a paramagnetic substance experiences a force when placed in a non-uniform magnetic field, causing an apparent change in its mass. This change can be measured using an analytical balance. The force acting on the sample is proportional to its magnetic susceptibility, which can be determined using the observed mass change and the known properties of the magnetic field. When a paramagnetic sample is placed in a magnetic field, it becomes magnetized due to the alignment of magnetic dipoles within the sample. The degree of this magnetization depends on the material's magnetic susceptibility, χm. The force on the sample in a magnetic field gradient can be expressed as:

F = (χm × V × H × dH/dx) / μ₀

Where V is the volume of the sample and dH/dx is the gradient of the magnetic field. In practice, this force is measured as an apparent change in the mass of the sample on the balance.