enEnglishguગુજરાતી
JEE Mains · Physics · STD 12 - 4. Moving charges and magnetism
A current \(i\) is flowing in a straight conductor of length \(L.\) The magnetic induction at a point on its axis at a distance \(\frac {L}{4}\) from its centre will be
- A \(\frac{{4{\mu _0}i}}{{\sqrt 5 \pi L}}\)
- B \(\frac{{{\mu _0}i}}{{2\pi L}}\)
- C \(\frac{{{\mu _0}i}}{{\sqrt 2 L}}\)
- D \(Zero\)
Answer & Solution
Correct Answer
(A) \(\frac{{4{\mu _0}i}}{{\sqrt 5 \pi L}}\)
Step-by-step Solution
Detailed explanation
\(B=\frac{\mu_{0} i}{4 \pi R}\left(\sin \theta_{1}+\sin \theta_{2}\right)\) \(\sin \theta_{2}=\frac{L / 2}{\sqrt{(L / 2)^{2}+(L / 2)^{2}}}=\frac{1}{2(\sqrt{1 / 4+1 / 16})}=\frac{2}{\sqrt{5}}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A copper rod of cross-sectional area \(A\) carries a uniform current \(I\) through it. At temperature \(T\), if the volume charge density of the rod is \(\rho \), how long will the charges take to travel a distance \(d\) ?JEE Mains 2018 Medium
- The equation for real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \(\mathrm{ab}^{-2}\) is equivalent to that of :JEE Mains 2025 Medium
- A bob of mass ' \(m\) ' is suspended by a light string of length ' \(L\) '. It is imparted a minimum horizontal velocity at the lowest point \(A\) such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \(\frac{(\text { K.E. })_A}{(\text { K.E. })_B}\) is _______.
JEE Mains 2024 Hard - Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' \(R\) ' is placed inside a large square loop of wire of side \(L\) \(( L \gg R )\). The loops are coplanar and their centres coincide :
JEE Mains 2023 Medium - A uniform thin rope of length \(12\, m\) and mass \(6\, kg\) hangs vertically from a rigid support and a block of mass \(2\, kg\) is attached to its free end. A transverse short wavetrain of wavelength \(6\, cm\) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \(cm\) ) when it reaches the top of the rope \(?\)JEE Mains 2020 Medium
- The height of victoria falls is \(63\, {m}\). What is the difference in temperature of water at the top and at the bottom of fall ? (In \(^{\circ} {C}\)) [Given \(1\, {cal}=4.2\, {J}\) and specific heat of water \(\left.=1 \,{cal} \,{g}^{-1}\;{ }^{\circ}\, {C}^{-1}\right]\)JEE Mains 2021 Medium
More PYQs from JEE Mains
- A laser beam has intensity of \( 4.0\times10^{14} W/m^{2} \). The amplitude of magnetic field associated with beam is__________ T. (Take \( \epsilon_{0}=8.85\times10^{-12} C^{2}/Nm^{2} \) and \( c=3\times10^{8} m/s \))JEE Mains 2026 Easy
- Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density \(d.\) The area of the base of both vessels is \(S\) but the height of liquid in one vessel is \(x_{1}\) and in the other, \(x_{2}\). When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process isJEE Mains 2020 Hard
- Let \(A (1,4)\) and \(B (1,-5)\) be two points. Let \(P\) be a point on the circle \((x-1)^{2}+(y-1)^{2}=1\) such that \(( PA )^{2}+( PB )^{2}\) have maximum value, then the points \(P , A\) and \(B\) lie on ...... .JEE Mains 2021 Hard
- Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of \(\mu_{A}\) to \(\mu_{B}\) is \(1: 2\). Then the thickness of material, in meter is: (Given \(v_{A}\) and \(v_{B}\) are velocities of light in \(A\) and \(B\) materials respectively).JEE Mains 2022 Hard
- If \(2\) mole of an ideal monoatomic gas at temperature \(T\), is mixed with \(6\) mole of another ideal monoatomic gas at temperature \(2T\) then the temperature of mixture is :JEE Mains 2026 Medium
- Identify the correct truth table of the given logical circuit.
JEE Mains 2026 Medium