Question
Write the formula for the force per unit length between two parallel current carrying wires. Using it, write the definition of Ampere and Coulomb.
✓
Answer
→As shown in the figure, two long wires $a$ and $b$ are placed parallel. The (perpendicular) distance between them is $d$. The current passing through them are $I _a$ and $I _b$ respectively.
→The force exerted by wire $a$ on a segment of length L on wire $b$ is
$F _{b a}=\frac{\mu_0 I _a I _b L}{2 \pi d}$
→Force per unit length
$f_{b a}=\frac{ F _{b a}}{L}=\frac{\mu_0 I _a I _b}{2 \pi d}$
→Similarly,
$f_{a b}=\frac{ F _{a b}}{L}=\frac{\mu_0 I _a I _b}{2 \pi d}$
→If we take $I _a= I _b=1 A$ and $d=1 m$ in above equation then
$f_{a b}=f_{b a}=2 \times 10^{-7} N$
→Definition of 1 Ampere : "The ampere is the value of that steady current which, when maintained in each of the two very long, straight, parallel conductors of negligible cross-section, and placed one metre apart in vacuum, would produce on each of these conductors a force equal to $2 \times 10^{-7}$ Newtons per metre of length."
→1 Coulomb : "When a steady current of 1 A is set up in a conductor, the amount of charge passing through its cross-section in 1 s is 1 coulomb."
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The charge on a proton is $+1.6 \times 10^{-19}C$ and that on an electron is $-1.6 \times 10^{-19}C.$ Does it mean that the electron has a charge $3.2 \times 10^{-19}C$ less than the charge of a proton?
→If the radius of the nucleus of $Al ^{27}$ is 3.6 Fermi , then what will be the radius of the $Fe ^{125}$ nucleus?
→A current I is flowing in an infinitely long conductor bent into the shape shown in Fig. If the radius of the curved part is R, find the magnetic field at the centre O.
A calorimeter is kept in a wooden box to insulate it thermally from the surroundings. Why is it necesaary?
A compound microscope consists of an objective lens of focal length 1 cm , an eyepiece of focal length 2 cm and tube length is 20 cm . Find its magnification.
Two point charges of $+10 \mu C$ and $-10 \mu C$ are kept at a distance of 40 cm from each other in air.(a) Calculate the electrical potential energy of the system. Assume that the electric potential energy at infinity is zero.(b) Draw the equipotential surface for the system.(c) How much work will have to be done to separateboth the charges of the system to infinity?
→A staircase contains three steps each 10cm high and 20cm wide (figure). What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane?
The peak power consumed by a resistive coil, when connected to an AC source, is 80W. Find the energy consumed by the coil in 100 seconds, which is many times larger than the time period of the source.
The ground state energy of hydrogen atom is – 13·6 eV. If an electron makes a transition from an energy level – 1·51 eV to – 3·4 eV, calculate the wavelength of the spectral line emitted and name the series of hydrogen spectrum to which it belongs.
The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectron emitted?