Learn Unit 3-Magnetic Effect of Current & Magnetism with Top Tutors

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In this diagram, the loop carrying current is represented by the straight lines forming the loop. The magnetic field lines form concentric circles around the loop, indicating the direction of the magnetic field. According to the right-hand rule, the direction of the magnetic field lines can be determined by curling the fingers of the right hand in the direction of the current flow around the loop. The thumb then points in the direction of the magnetic field lines inside the loop.

To generalize Ampere's circuital law to include the term due to displacement current, we use Maxwell's modification of Ampere's law, which states:

∮B⋅dl=μ0(∬J⋅dA+ε0dtd∬E⋅dA)

Where:

• BB is the magnetic field,
• dldl is an infinitesimal element of the closed path,
• μ0μ0 is the permeability of free space,
• JJ is the current density,
• dAdA is an infinitesimal element of area,
• ε0ε0 is the permittivity of free space,
• EE is the electric field.

 This modification includes the term ε0ddt∬E⋅dAε0dtd∬E⋅dA, which accounts for the displacement current.

The expression for the magnitude of the magnetic field at the center of a circular loop of radius rr carrying a steady current II can be derived using Ampere's law or Biot-Savart's law. For a circular loop, the magnetic field at its center is given by:

B=μ0I2rB=2rμ0I

Where:

• BB is the magnitude of the magnetic field,
• μ0μ0 is the permeability of free space (4π×10−7 T⋅m/A4π×10−7T⋅m/A),
• II is the current flowing through the loop,
• rr is the radius of the loop.

The direction of the magnetic field at the center of the loop is perpendicular to the plane of the loop and is along the axis passing through the center of the loop.

Now, let's draw the magnetic field lines due to the current loop:
         ____B____
       /             \
     /                 \
   /                     \
  |         \     /       |
  |           \ /         |
  |           / \         |
  |         /     \       |
   \                     /
     \                 /
       \____B______/

In this diagram, the loop is represented by the circle with current flowing clockwise. The magnetic field lines form concentric circles around the loop, with their direction indicated by arrows. At the center of the loop, the magnetic field lines are directed perpendicular to the plane of the loop.