MHT CET · Physics · Magnetic Effects of Current
A long straight conductor is bent into shape as shown. If it carries \(1 \mathrm{~A}\) and its radius is \(R\), then magnetic ficld \(B\) at the centre of circular coil
- A \(\infty\)
- B Zero
- C \(\frac{\mu_{0} i(\pi+1)}{2 \pi R}\)
- D \(\frac{\mu_{0} i(\pi-1)}{2 \pi R}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mu_{0} i(\pi-1)}{2 \pi R}\)
Step-by-step Solution
Detailed explanation
Magnetic field at centre \(O=\) magnetic field due to reaction \(A B+\) magnetic field due to section \(P Q R\)
\(
B_{0}=B_{A B}+B_{P Q R}
\)
but \(B_{A B}=\frac{\mu_{0} i}{2 \pi R}\) (upside the plane of paper)
and \(B_{P Q R}=\frac{\mu_{0} i}{2 R}\) (inside the plane of paper)
Hence \(B_{0}=\frac{\mu_{0} i}{2 R}-\frac{\mu_{0} i}{2 \pi R}\)
\(
B_{0}=\frac{\mu_{0} i(\pi-1)}{2 \pi R}
\)
\(
B_{0}=B_{A B}+B_{P Q R}
\)
but \(B_{A B}=\frac{\mu_{0} i}{2 \pi R}\) (upside the plane of paper)
and \(B_{P Q R}=\frac{\mu_{0} i}{2 R}\) (inside the plane of paper)
Hence \(B_{0}=\frac{\mu_{0} i}{2 R}-\frac{\mu_{0} i}{2 \pi R}\)
\(
B_{0}=\frac{\mu_{0} i(\pi-1)}{2 \pi R}
\)
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
- The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by \(48^{\circ} \mathrm{C}\) at constant pressure is (Molecular weight of nitrogen \(=28, R=\) gas constant, \(C_p=\frac{7}{2} R\) for diatomic gas)MHT CET 2025 Easy
- An A.C. circuit contains resistance of \(12 \Omega\) and inductive reactance \(5 \Omega\). The phase
angle between current and potential difference will beMHT CET 2020 Medium - In Young's double slit experiment let 'd' be the distance between two slits and 'D' be the distance between the slits and the screen. Using a monochromatic source of wavelength ' \(\lambda\) ', in an interference pattern, third minimum is observed exactly in front of one of the slits. If at the same point on the screen first minimum is to be obtained, the required change in the wavelength is [d & D are not changed]MHT CET 2025 Medium
- The ratio of energy required to raise a satellite of mass ' \(\mathrm{m}\) ' to height ' \(h\) ' above the earth's surface to that required to put it into the orbit at same height is \([\)\(\mathrm{R}=\) radius of earth\(]\)MHT CET 2021 Medium
- Rate of flow of heat through a cylindrical rod is ' \(\mathrm{H}_1\) '. The temperature at the ends of the rod are ' \(T_1\) ' and ' \(T_2\) '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' \(\mathrm{H}_2\) '. ThenMHT CET 2024 Easy
- A mass ' \(m\) ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg , the period increases by 3 second. The initial mass ' m ' is equal toMHT CET 2024 Medium
More PYQs from MHT CET
- In the logic circuit diagram, A, B and C are the inputs, \(\mathrm{Y}\) is the output. The output \(\mathrm{Y}\) is ' \(\mathrm{HIGH}\) '
MHT CET 2022 Easy - What is the numerical difference in molar masses of second and third member of a homologous series?MHT CET 2024 Easy
- The distance of the point \((1,2)\) from the line \(x+y=0\) measured parallel to the line \(3 x-y=2\) isMHT CET 2025 Medium
- The value of \(\sin \left[\tan ^{-1}\left(\frac{1-x^2}{2 x}\right)+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right]\) isMHT CET 2025 Medium
- Which among the following statements about \(\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}\) is NOT true?MHT CET 2021 Medium
- The maximum volume of a right circular cylinder if the sum of its radius and height is
\(6 \mathrm{~m}\) isMHT CET 2020 Easy