MHT CET · Physics · Magnetic Effects of Current
Two wires of same length are made to from a circle and a square. They carry same current. The ratio of the magnetic moment of circle to that of square is
- A \(4: \pi\)
- B \(2: \pi\)
- C \(\pi: 4\)
- D \(\pi: 2\)
Answer & Solution
Correct Answer
(A) \(4: \pi\)
Step-by-step Solution
Detailed explanation
Let length of wire be \(l\). For a square loop, side of square \(\frac{l}{4}\).
Hence its magnetic moment
\(M_{\mathrm{sq}}=i A=i\left[\frac{l}{4}\right]^2=\frac{i l^2}{16}\)
Radius of a circular loop \(r=\frac{l}{2 \pi}\)
Hence, its magnetic moment
\(\begin{aligned} & M_{\mathrm{cir}}=i A=i \pi r^2 \\ & M_{\text {cir }}=i \pi\left[\frac{l^2}{4 \pi r^2}\right]=\frac{i l^2}{4 \pi} \\ & \Rightarrow \frac{M_{\text {cir }}}{M_{\mathrm{sq}}}=\frac{4}{\pi}\end{aligned}\)
Hence its magnetic moment
\(M_{\mathrm{sq}}=i A=i\left[\frac{l}{4}\right]^2=\frac{i l^2}{16}\)
Radius of a circular loop \(r=\frac{l}{2 \pi}\)
Hence, its magnetic moment
\(\begin{aligned} & M_{\mathrm{cir}}=i A=i \pi r^2 \\ & M_{\text {cir }}=i \pi\left[\frac{l^2}{4 \pi r^2}\right]=\frac{i l^2}{4 \pi} \\ & \Rightarrow \frac{M_{\text {cir }}}{M_{\mathrm{sq}}}=\frac{4}{\pi}\end{aligned}\)
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
- Sound waves are not transmitted a long distance becauseMHT CET 2007 Medium
- A sonometer wire \(49 \mathrm{~cm}\) long is in unison with a tuning fork of frequency ' \(n\) '. If the length of the wire is decreased by \(1 \mathrm{~cm}\) and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of ' \(n\) ' isMHT CET 2023 Medium
- The fundamental frequency of an air column in a pipe open at both ends is ' \(\mathrm{f}_1\) '. Now \(80 \%\) of its length is immersed in water, the fundamental frequency of the air column becomes \(f_2\). The ratio of \(f_1: f_2\) isMHT CET 2024 Medium
- For a light ray to undergo total internal reflection, light must travel from ( \(i\) = angle of incidence,\(i_C=\) critical angle \()\)MHT CET 2022 Easy
- Magnetic susceptibility of a paramagnetic substance isMHT CET 2019 Easy
- Consider the following statement about electric field intensity and electric potential.
A. The electric field intensity due to a charged spherical shell is inversely proportional to square of its radius.
B. The electric potential due to a point charge is inversely proportional to the distance between charge and the point.MHT CET 2022 Easy
More PYQs from MHT CET
- For all real \(\mathrm{x}\), the minimum value of the function \(f(x)=\frac{1-x+x^2}{1+x+x^2}\) isMHT CET 2021 Easy
- What is the number of moles of water removed from one mole of cane sugar when charred completely using conc. \(\mathrm{H}_2 \mathrm{SO}_4\) ?MHT CET 2022 Easy
- Two rings of radius ' \(R\) ' and ' \(n R\) ' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is \(1: 8\). The value of ' \(n\) ' is (mass per unit length \(=\lambda\) )MHT CET 2021 Easy
- Which hormone is reported from Banana flowers?MHT CET 2022 Easy
- The number of integral values of \(K\) for which \(x^2+\mathrm{y}^2+\mathrm{k} x+(1-\mathrm{k}) \mathrm{y}+5=0\) represents a circle whose radius cannot exceeds 5, areMHT CET 2025 Medium
- A sheet of steel is 40 cm long and 5 cm broad at \(0^{\circ} \mathrm{C}\). The surface area of the sheet increases by \(1.4 \mathrm{~cm}^2\) at \(100^{\circ} \mathrm{C}\). Coefficient of linear expansion of steel isMHT CET 2024 Medium