Question

marks: 7
ing, c) Write ampere's circuital law.
d) Write ohm's law in vector form​

Answer 1

Solution:-

a). The electrical force on a charge is related to the electric field ( caused by other charge ) by the equation

$\implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \rm{F_e }= q \rm \: E$

Just like gravitational force , the static electrical force is a conservative force .this means that the work done by the static electric force around any closed path is zero

$\implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: q \oint \: E.dl \: = 0j$

Hence we have

$\implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \oint E.dl = 0v$

In the other , the intergral of the static electric field around a closed path is zero what about the integral of the magnetic field around closed path? that is we want to determine the value of

$\implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \oint \: B.dl$

Hence we have to be careful .the quantity B. d I doesn't represent some physical quantity and certainly not work . although the static magnetic force does no work on a moving charge , we cannot conclude that the path integral of the magnetic field around a closed path is zero . we are just curious about what this analogous line integral amounts to .

$\rm \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \oint \: B.dI = \mu_o(i_{net})$

This is known as Ampere circuital law

b ) Ohm law in vector form

The vector form of Ohm’s law is used in electromagnetics and material science. The vector form is given as,

J = σ E

Where,

– represents vector

J is the current density,Eis the electric field and σ is conductivity.