MCQ
Two infinitely long parallel wires having linear charge densities ${\lambda _1}$ and ${\lambda _2}$ respectively are placed at a distance of $R$ metres. The force per unit length on either wire will be $\left( {K = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$
  • A
    $K\frac{{2{\lambda _1}{\lambda _2}}}{{{R^2}}}$
  • $K\frac{{2{\lambda _1}{\lambda _2}}}{R}$
  • C
    $K\frac{{{\lambda _1}{\lambda _2}}}{{{R^2}}}$
  • D
    $K\frac{{{\lambda _1}{\lambda _2}}}{R}$

Answer

Correct option: B.
$K\frac{{2{\lambda _1}{\lambda _2}}}{R}$
b
(b) Force on $l$ length of the wire $2$ is
${F_2} = Q{E_1} = ({\lambda _2}l)\frac{{2k{\lambda _1}}}{R}$
$==>$ $\frac{{{F_2}}}{l} = \frac{{2k{\lambda _1}{\lambda _2}}}{R}$
Also $\frac{{{F_1}}}{l} = \frac{{{F_2}}}{l} = \frac{F}{l} = \frac{{2k{\lambda _1}{\lambda _2}}}{R}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A wire has resistance $12\,\Omega $. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to ................ $\Omega$
Assertion : The air bubble shines in water.
Reason : Air bubble in water shines due to refraction of light
A positive charge $q$ is kept at the center of a thick shell of inner radius $R_1$ and outer radius $R_2$ which is made up of conducting material. If $\phi_1$ is flux through closed gaussian surface $S_1$ whose radius is just less than $R_1$ and $\phi_2$ is flux through closed gaussian surface $S_2$ whose radius is just greater than $R_1$ then:-
Two capacitors $C_1 = 4\  \mu F$ and $C_2 = 2\ \mu F$ are charged to same potential $ V = 500\  Volt$, but with opposite polarity as shown in the figure. The switches $S_1$ and $S_2$ are closed.
In an adjoining figure are shown three capacitors $C_1,C_2$ and $C_3$ joined to a battery. The correct condition will be (Symbols have their usual meanings)
A magnetic dipole is under the influence of two magnetic fields The angle between the field directions is $60^{\circ}$ and one of the fields has a magnitude of $1.2 \times 10^{-2} T$. If the dipole comes to stable equilibrium at an angle of $15^{\circ}$ with this field, what is the magnitude of other field?
Which of the following can be used in cancer treatment?
A capacitor consists of two parallel plates, with an area of cross-section of $0.001 m^2$, separated by a distance of 0.0001 m. If the voltage across the plates varies at the rate of $10^8 V / s$, then the value of displacement current through the capacitor is
A sample of radioactive element has a mass of 10 gm at an instant t = 0.The approximate mass of this element in the sample after two mean lives is
A ferromagnetic material is heated above its curie temperature. Which one is a correct statement