Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
Solution and Explanation
Current flowing in wire B, \(I_B = 5.0 A\)
Distance between the two wires, \(r = 4.0 \,cm = 0.04 \,m \)
Length of a section of wire A, \(L = 10 \,cm = 0.1 \,m\)
Force exerted on length L due to the magnetic field is given as:
\(F = \frac{μ_0I_AI_BL}{2πr}\)
Where, \(μ_0\) = Permeability of free space = \( 4π \times 10^7\, TmA^{-1}\)
\( F= \frac{4π \times 10^{-7} \times 8 \times 5 \times 0.1}{2π \times0.04 } = 2 \times 10^{-5 }N\)
The magnitude of force is \(2 × 10^{–5 }N\). This is an attractive force normal to A towards B because the direction of the currents in the wires is the same.
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Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.