# Displacement Current

• The magnetic field due to current carrying conductor, ic is determined by using the Ampere’s circuit law.

\tt \int \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_{0} i_{c}

• Conduction current, ic is produced by the time varying magnetic field \tt i_{c} \propto \frac{dB}{dt} \ and \ i_{c} = \frac{dq}{dt}
• The rate of change of electrical flux produces a current called DISPLACEMENT CURRENT, id.
• Flux due to electric field. φE = EA Cos θ
• \tt \overline{E} \cdot \overline{A} = \int \overline{E} \cdot \overline{ds}
• \tt i_{d} = \varepsilon_{0} \frac{d \phi_{E}}{dt}
• \tt i_{d} = \varepsilon_{0} A \frac{dE}{dt} {φ = E.A}
• When a variable electrical field is applied to the gap.

\tt i_{d} = A \varepsilon_{0} \frac{dE}{dt}                                     id = Displacement Current

• When a variable potential difference is applied to the plates of a condenser C then \tt i_{d} = C \frac{dv}{dt}
• \tt i_{c} = i_{d} \Rightarrow i_{c} = \frac{V}{X_{c}} = V \omega C
where, ic = conduction current,  id = displacement current
• Amperes circuit law \tt \int \overrightarrow{B} \cdot \overrightarrow{dl} = \mu_{0} \left(i_{c} + i_{d}\right)

= \tt \mu_{0} \left(i_{c} + \varepsilon_{0} \frac{d \phi_{E}}{dt}\right)

• \tt \int B \cdot dl = \mu_{0}i_{c} + \mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{dt}
• \tt B = \frac{\mu_{0}}{2 \pi} i_{d} \frac{r}{R^{2}}
• The magnetic field at a distance R from the axis \tt B = \frac{\mu_{0}}{2 \pi} \frac{i_{d}}{R}. This is the maximum value.
• GAUSS LAW FOR ELECTRICITY \tt \int \overrightarrow{E} . \overrightarrow{dA} = q_{net}/ \varepsilon_{0}
• GAUSS LAW FOR MAGNETISM \tt \int \overrightarrow{B} . \overrightarrow{dA} = 0
\tt \int \overrightarrow{E} . \overrightarrow{dl} = - \frac{d \phi_{B}}{dt}
• \tt \int \overrightarrow{B} . \overrightarrow{dl} = \mu_{0}i_{c} + \mu_{0} \varepsilon_{0} \frac{d \phi_{E}}{dt} = \mu_{0} \left(i_{c} + i_{d}\right)
• The force acting on a charge, of moving in electric and magnetic fields which are similar to EM wave are existing simultaneously is \tt \overline{F} = q \left[ \overline{E} + \overline{V} \times \overline{B}\right]. This force is Lorentz force.

### View the Topic in this video From 00:34 To 57:46

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

1. According to Ampere's circuital law, the magnetic field B is related to steady current I as
\oint_{c} \overrightarrow{B}\cdot \overrightarrow{dl} = \mu_{0}I

2. The sum of the conduction current and the displacement current. The generalised law is \oint B· dI\mu_{0}i_{c} + \mu_{0} \varepsilon_{0}\frac{d \phi_{E}}{dt}

3. \oint E·dA = Q/ε0 (Gauss's Law for electricity)

4. \oint B·dA = 0 (Gauss's Law for Magnetism)

5. \oint E·dl = \frac{-d \phi_{B}}{dt}(Faraday's Law)