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Determine the force required to separate two magnetic surfaces with a contact area of 4π cm 2 and the magnetic flux density across the surface is 1 wb/m 2 .
800 N
500 N
1000 N
100 N
500 N
The force of attraction between two magnetic surfaces is directly proportional to the square of the magnetic flux density and the contact area. Using the standard magnetic pull formula, the force is calculated as F=2μ0B2A, where B is the flux density, A is the area, and μ0 is the permeability of free space.
The force of attraction between two magnetic surfaces is directly proportional to the square of the magnetic flux density and the contact area. Using the standard magnetic pull formula, the force is calculated as F=2μ0B2A, where B is the flux density, A is the area, and μ0 is the permeability of free space.
F=2μ0B2A — Force in Newtons
A=4π×10−4 m2 — Conversion of area to SI units
μ0=4π×10−7 H/m — Permeability of free space
When a magnetic field passes through an interface of two surfaces, the magnetic pressure creates a tensile force tending to pull the surfaces together. This is analogous to electrostatic pressure, where the energy stored in the magnetic field per unit volume is 2μ0B2. By multiplying this energy density by the volume associated with the interface (Area × distance), the force derived is F=2μ0B2A.
The magnetic pull is proportional to the square of the flux density B.
Area must be converted from cm2 to m2 before substitution.
The constant μ0 is essential for force calculation in air gaps.
High holding force for small surface areas
Instantaneous control via magnetic excitation
Residual magnetism may prevent separation
Highly sensitive to the air gap size
Electromagnetic chucks
Solenoid actuators
Calculation: F=2×4π×10−712×4π×10−4=2×10−710−4=0.5×103=500 N.
Common error: Failing to convert 4π cm2 to 4π×10−4 m2 leads to incorrect magnitude results.
B is correct — The calculated force based on the magnetic pull formula F=2μ0B2A results in exactly 500 N.
Always ensure units are in SI before applying electromagnetic formulas; failing to convert area from cm2 to m2 is a frequent trap in competitive exams.
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