JEE Mains · Physics · STD 12 - 4. Moving charges and magnetism
The region between \(y = 0\) and \(y = d\) contains a magnetic field \(\vec B = B\hat z\) A particle of mass \(m\) and charge \(q\) enters the region with a velocity \(\vec v = v\hat i\). If \(d = \frac{{mv}}{{2qB}}\) , the acceleration of the charged particle at the point of its emergence at the other side is
- A \(\frac{{qvB}}{m}\,\left( {\,\frac{{ \hat j + \hat i}}{{\sqrt 2 }}} \right)\)
- B \(\frac{{qvB}}{m}{\mkern 1mu} \left( {{\mkern 1mu} \frac{{\sqrt 3 }}{2}{\mkern 1mu} \hat i + \frac{1}{2}\hat j} \right)\)
- C \(\frac{{qvB}}{m}\,\left( {\,\frac{{ - \hat j + \hat i}}{{\sqrt 2 }}} \right)\)
- D \(\frac{{qvB}}{m}{\mkern 1mu} \left( {\frac{1}{2}\hat j - \frac{{\sqrt 3 }}{2}\hat i} \right)\)
Answer & Solution
Correct Answer
(D) \(\frac{{qvB}}{m}{\mkern 1mu} \left( {\frac{1}{2}\hat j - \frac{{\sqrt 3 }}{2}\hat i} \right)\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{B}}=\mathrm{B} \hat{\mathrm{k}}\) \(r=\frac{m v}{q B}\) \(r=2 d\) \(\sin \theta=\frac{d}{2 d} \Rightarrow \sin \theta=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{6}\) \(\vec{a}=\frac{|q| v b}{m}(\cos \theta(-\hat{i})+\sin \theta \hat{j})\)…
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
- Photons of an electromagnetic radiation has an energy \(11\, keV\) each. To which region of electromagnetic spectrum does it belong ?JEE Mains 2013 Medium
- For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is ................JEE Mains 2023 Medium
- A current of \(200\ \mu \mathrm{A}\) deflects the coil of a moving coil galvanometer through \(60^{\circ}\). The current to cause deflection through \(\frac{\pi}{10}\) radian is:JEE Mains 2024 Hard
- An ideal gas undergoes a process maintaining relation between pressure \((P)\) and volume \((V)\) as \(P = P_o\left(1 + \left(\dfrac{V_o}{V}\right)^2\right)^{-1}\), where \(P_o\) and \(V_o\) are constants. If two samples \(A\) and \(B\) (two moles each) with initial volumes \(V_o\) and \(3V_o\) respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, \(T_B - T_A\) is _____. (\(R = \) gas constant)JEE Mains 2026 Hard
- Taking the wavelength of first Balmer line in hydrogen spectrum (\( n = 3\) to \(n = 2\) ) as \(660\,nm ,\) the wavelength of the \(2^{nd}\) Balmer line ( \(n =4\) to \(n = 2\) ) will be....\(nm\)JEE Mains 2019 Hard
- A long straight wire of circular cross-section (radius \(a\)) is carrying steady current \(I\). The current \(I\) is uniformly distributed across this cross-section. The magnetic field isJEE Mains 2023 Medium
More PYQs from JEE Mains
- Let \(A\) and \(B\) be two \(3 \times 3\) non-zero real matrices such that \(AB\) is a zero matrix. Then.JEE Mains 2022 Medium
- The angle between vector \(\vec{Q}\) and the resultant of \((2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})\) and \((2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})\) is _______.JEE Mains 2024 Hard
- Let \(f(x)=x^{6}+2 x^{4}+x^{3}+2 x+3, x \in R\). Then the natural number \(\mathrm{n}\) for which \(\lim _{x \rightarrow 1} \frac{\mathrm{x}^{\mathrm{n}} \mathrm{f}(1)-\mathrm{f}(\mathrm{x})}{\mathrm{x}-1}=44\) is ...... .JEE Mains 2021 Hard
- The minimum value of \(\alpha\) for which the equation \(\frac{4}{\sin x}+\frac{1}{1-\sin x}=\alpha\) has at least one solution in \(\left(0, \frac{\pi}{2}\right)\) is ..........JEE Mains 2021 Medium
- A water drop of radius \(1\,\mu m\) falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is \(1.8 \times 10^{-5}\,Nsm ^{-2}\) and its density is negligible as compared to that of water \(10^{6}\,gm ^{-3}\). Terminal velocity of the water drop is________ \(\times 10^{-6}\,ms ^{-1}\) (Take acceleration due to gravity \(=10\,ms ^{-2}\) )JEE Mains 2022 Medium
- Let \(A=\{0,1,2,3,4,5\}\). Let \(R\) be a relation on A defined by \((x, y) \in R\) if and only if max \(\{x, y\} \in\{3,4\}\). Then among the statements \(\left(\mathrm{S}_1\right)\) : The number of elements in R is 18 , and \(\left(\mathrm{S}_2\right)\) : The relation R is symmetric but neither reflexive nor transitiveJEE Mains 2025 Medium