Magnetic Field Laws & their Applications

1 Mark Question

1.Draw the magnetic field lines due to a current carrying loop. [Delhi 2013 C] Ans.

Magnetic field lines due to a current carrying loop are given by S (1)

2 Marks Questions

1. Considering the case of a parallel plate capacitor being charged, show how one is required

to generalise Ampere's circuital law to include the term due to displacement current. [All India 2014,2011]

Ans.

Ampere's circuital law conduction current during charging of a capacitor was found inconsistent. Therefore, Maxwell modified Ampere's circuital law by introducing displacement current. (1/2)

Ampere's circuital law <math>\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I</math> was modified to <math>\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 (I_R + I_D)</math>

It is called modified Ampere's circuital law or Ampere-Maxwell's circuital law.

The displacement current arising due to time varying electric field is given by <math>I_D = \varepsilon_0 \frac{d\phi_E}{dt}</math>

Therefore, modified Ampere's circuital law may be expressed as

<math display="block">

\oint \mathbf{B} \cdot d\mathbf{I} = \mu_0 \mathbf{I} \left( I_C + \varepsilon_0 \frac{d\phi_E}{dt} \right)

</math>

(1/2)

3.(i) State Biot-Savart's law in vector form expressing the magnetic field due to an element dl carrying current 7 at a distance r from the element.

1. Write the expression for the magnitude of the magnetic field at the centre of a circular

loop of radius r carrying a steady current 7. Draw the field lines due to the current loop.[All India 2014C]

Ans.(i)

Biot-Savart's law This law states that the magnetic field (dB) at point P due to small current element Idl of current carrying conductor is

1. directly proportional to the Idl (current) element of the conductor.

dB ∝ Idl

I dl χı