Question:

A straight wire of diameter 0.5 mm carrying a current of 1 A is replaced by the another wire of 1 mm diameter carrying the same current. The strength of the magnetic field far away is

Updated On: Aug 16, 2024
  • one-quarter of the earlier value
  • one-half of the earlier value
  • twice the earlier value
  • same as the earlier value
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The Correct Option is D

Solution and Explanation

Diameter of first wire $ (d_1) $ = 0.5 mm;
Current in first wire$ (I_1) $ = 1A; Diameter of second
wire $ (d_2) = 1 $ mm and current in second wire $ (I_2) = 1 A. $
Strength of magnetic field due to current flowing
in a conductor, $ (B) = \frac{{\mu}_0}{4 \pi } \times \frac{2I}{ a} \, \, or \, \, B \propto I $
Since the current in both the wires is same,
therefore there is no change in the strength of the
magnetic field.
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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.