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Moving Charges and Magnetism Set-4 MCQ Online Practice Test | Class 12 | Quiz Tweek

Moving Charges and Magnetism Set-4

Practice Important MCQs for Moving Charges and Magnetism — Physics, Class 12.

This chapter is central to Class 12 Physics because it links motion of charges with electric and magnetic effects—leading to core ideas like magnetic force, circular/helical motion, magnetic fields due to currents, and electromagnetic induction–style energy/force balance (e.g., braking). It is heavily asked in board exams and repeatedly tested in competitive exams through numerical problems and conceptual reasoning.

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Q1. An electron is accelerated from rest through a potential difference $V=500\ \mathrm{V}$ and then enters a region of uniform magnetic field $B=2.0\times10^{-3}\ \mathrm{T}$ with its velocity perpendicular to $\mathbf{B}$ . (Take $m_e=9.11\times10^{-31}\ \mathrm{kg}$ , $e=1.60\times10^{-19}\ \mathrm{C}$ .) The radius of the circular path is closest to:

(A)

$3.8\times10^{-1}\ \mathrm{m}$

(B)

$3.8\times10^{-2}\ \mathrm{m}$

(C)

$7.6\times10^{-3}\ \mathrm{m}$

(D)

$7.5\times10^{-2}\ \mathrm{m}$

Q2. An $\alpha$ –particle (mass $m=6.64\times10^{-27}\ \mathrm{kg}$ , charge $q=+2e$ ) has kinetic energy $K=3.2\times10^{-13}\ \mathrm{J}$ and enters a uniform magnetic field $B=0.20\ \mathrm{T}$ with its velocity making an angle $60^\circ$ with the field. Using $v=\sqrt{2K/m}$ , calculate the radius $r$ of the helical path (due to the perpendicular component) and the pitch (distance advanced along the field in one revolution).

(A)

$r\approx0.44\ \mathrm{m},\ \text{pitch}\approx1.6\ \mathrm{m}$

(B)

$r\approx1.76\ \mathrm{m},\ \text{pitch}\approx6.4\ \mathrm{m}$

(C)

$r\approx0.88\ \mathrm{m},\ \text{pitch}\approx1.6\ \mathrm{m}$

(D)

$r\approx0.88\ \mathrm{m},\ \text{pitch}\approx3.20\ \mathrm{m}$

Q3. A long straight wire carries current $I_1=10.0\ \mathrm{A}$ upward. A rectangular loop of height $h=4.0\ \mathrm{cm}$ and width $w=3.0\ \mathrm{cm}$ lies in the same plane; its nearest vertical side is at distance $a=2.0\ \mathrm{cm}$ from the wire. The loop carries current $I_2=5.0\ \mathrm{A}$ such that the current in the side nearest the wire also flows upward (i.e. same direction as the wire in that segment). Using $F/L=\dfrac{\mu_0 I_1 I_2}{2\pi r}$ for parallel currents, the net magnetic force on the loop is:

(A)

$1.2\times10^{-5}\ \mathrm{N}$ toward the wire

(B)

$1.2\times10^{-5}\ \mathrm{N}$ away from the wire

(C)

$2.0\times10^{-5}\ \mathrm{N}$ toward the wire

(D)

$1.2\times10^{-6}\ \mathrm{N}$ toward the wire

Q4. A conducting rod of mass $m=0.50\ \mathrm{kg}$ and length $L=0.20\ \mathrm{m}$ slides without friction on parallel rails forming a closed circuit with resistance $R=2.0\ \Omega$ . A uniform magnetic field $B=0.50\ \mathrm{T}$ is perpendicular to the plane of the rails. A constant horizontal force $F=1.0\ \mathrm{N}$ pulls the rod to the right. Accounting for the motional emf $\mathcal{E}=BLv$ and the magnetic braking force $F_{\rm mag}=\dfrac{B^2L^2}{R}v$ , find (i) the terminal speed $v_t$ and (ii) the time constant $\tau$ for approach to $v_t$ (starting from rest).

(A)

$v_t=200\ \mathrm{m/s},\ \tau=50\ \mathrm{s}$

(B)

$v_t=20\ \mathrm{m/s},\ \tau=100\ \mathrm{s}$

(C)

$v_t=200\ \mathrm{m/s},\ \tau=100\ \mathrm{s}$

(D)

$v_t=2000\ \mathrm{m/s},\ \tau=100\ \mathrm{s}$

Q5. A proton (mass $m_p$ , charge $+e$ ) and an alpha particle (mass $4m_p$ , charge $+2e$ ) are given the same kinetic energy $K$ and then enter a uniform magnetic field $\mathbf{B}$ perpendicular to their velocities. Using $r=\dfrac{\sqrt{2Km}}{qB}$ and $\omega=\dfrac{qB}{m}$ , which statement is correct?

(A)

Their radii are equal; the alpha's cyclotron frequency is half that of the proton.

(B)

Their radii are equal; the alpha and proton have the same cyclotron frequency.

(C)

The alpha's radius is half the proton's; the alpha and proton have the same cyclotron frequency.

(D)

The proton's radius is twice the alpha's; the alpha's cyclotron frequency is half that of the proton.

Q6. An electron with speed $2.0\times10^{6}\ \mathrm{m\,s^{-1}}$ moves through a uniform magnetic field of magnitude $0.20\ \mathrm{T}$ . Its velocity makes an angle of $30^\circ$ with the field. What is the magnitude of the magnetic force on the electron? (Take $e=1.60\times10^{-19}\ \mathrm{C}$ .)

(A)

$6.4\times10^{-15}\ \mathrm{N}$

(B)

$1.28\times10^{-13}\ \mathrm{N}$

(C)

$3.2\times10^{-14}\ \mathrm{N}$

(D)

$3.2\times10^{-15}\ \mathrm{N}$

Q7. An electron is accelerated from rest through a potential difference $V=200\ \mathrm{V}$ and then enters a uniform magnetic field $B=2.0\times10^{-3}\ \mathrm{T}$ such that the angle between its velocity and the field is $30^\circ$ . Calculate the radius of the circular component of its helical path (i.e. radius corresponding to the velocity component perpendicular to the field). (Use $m_e=9.11\times10^{-31}\ \mathrm{kg}$ and $e=1.60\times10^{-19}\ \mathrm{C}$ .)

(A)

$1.19\times10^{-2}\ \mathrm{m}$

(B)

$1.19\times10^{-1}\ \mathrm{m}$

(C)

$1.19\times10^{-3}\ \mathrm{m}$

(D)

$2.38\times10^{-2}\ \mathrm{m}$

Q8. A conducting rod of length $L=0.50\ \mathrm{m}$ slides without friction on two parallel horizontal conducting rails connected by a resistor $R=1.0\ \Omega$ , forming a closed circuit. A uniform magnetic field $B=0.50\ \mathrm{T}$ is directed into the plane of the rails. A constant horizontal force $F=0.20\ \mathrm{N}$ is applied to the rod; after transients it moves with constant speed $v$ . Assuming motional emf and steady current, determine $v$ .

(A)

$1.60\ \mathrm{m\,s^{-1}}$

(B)

$0.64\ \mathrm{m\,s^{-1}}$

(C)

$6.40\ \mathrm{m\,s^{-1}}$

(D)

$3.20\ \mathrm{m\,s^{-1}}$

Q9. A proton ( $m_p=1.67\times10^{-27}\ \mathrm{kg}$ , $e=1.60\times10^{-19}\ \mathrm{C}$ ) moves along the $x$ -axis with speed $v=1.0\times10^{6}\ \mathrm{m\,s^{-1}}$ and enters a region between $x=0$ and $x=w$ where a uniform magnetic field $B=1.0\times10^{-2}\ \mathrm{T}$ points in the $+z$ -direction. If $w=0.20\ \mathrm{m}$ , find the transverse ( $y$ ) displacement of the proton when it exits the region at $x=w$ (neglect edge effects).

(A)

$9.56\times10^{-3}\ \mathrm{m}$

(B)

$1.91\times10^{-2}\ \mathrm{m}$

(C)

$3.82\times10^{-2}\ \mathrm{m}$

(D)

$1.20\times10^{-1}\ \mathrm{m}$

Q10. A very long straight wire carries a steady current $I$ to the right and also has a uniform positive linear charge density $\lambda$ . A positive test charge moves parallel to the wire (in the same direction as $I$ ) at distance $r$ from the wire with speed $v$ . For what value of $v$ (in terms of $\lambda,I,\epsilon_0,\mu_0$ ) will the net radial force on the moving charge be zero?

(A)

$v=\dfrac{\lambda}{2\pi\,\epsilon_0\mu_0\,I}$

(B)

$v=\dfrac{\mu_0\,I}{\epsilon_0\,\lambda}$

(C)

$v=\dfrac{\lambda}{\epsilon_0\mu_0\,I}$

(D)

$v=\dfrac{\lambda}{\mu_0\,I}$

Q11. A proton of mass $m_p=1.67\times10^{-27}\ \mathrm{kg}$ and charge $e=1.60\times10^{-19}\ \mathrm{C}$ enters a uniform magnetic field of magnitude $B=0.05\ \mathrm{T}$ with speed $v=2.00\times10^{6}\ \mathrm{m\,s^{-1}}$ at an angle $60^\circ$ to the field. What is the radius of the circular motion due to the component of velocity perpendicular to the field?

(A)

$0.18\ \mathrm{m}$

(B)

$0.36\ \mathrm{m}$

(C)

$0.72\ \mathrm{m}$

(D)

$0.12\ \mathrm{m}$

Q12. A long straight wire carries current $I=10.0\ \mathrm{A}$ . A rectangular loop of width $a=0.10\ \mathrm{m}$ (side parallel to the wire) and height $b=0.20\ \mathrm{m}$ lies coaxial and coplanar with the wire so that the side of the loop closest to the wire is at distance $d=0.05\ \mathrm{m}$ from it. The loop carries current $i=2.00\ \mathrm{A}$ with the current in the nearer side flowing in the same direction as $I$ in the straight wire. Neglecting forces on the short sides, the net magnetic force on the entire rectangular loop is:

(A)

$9.6\times10^{-6}\ \mathrm{N}$ toward the wire

(B)

$3.2\times10^{-6}\ \mathrm{N}$ toward the wire

(C)

$6.4\times10^{-6}\ \mathrm{N}$ away from the wire

(D)

$6.4\times10^{-6}\ \mathrm{N}$ toward the wire

Q13. A proton ( $m_p=1.67\times10^{-27}\ \mathrm{kg}$ , $e=1.60\times10^{-19}\ \mathrm{C}$ ) moves with velocity $v=3.00\times10^{6}\ \mathrm{m\,s^{-1}}$ along the $x$ -axis and enters a region $0<x<L$ where a uniform magnetic field $\vec{B}$ of magnitude $B=0.020\ \mathrm{T}$ points into the page. The region length is $L=0.100\ \mathrm{m}$ . If the proton's velocity is perpendicular to $\vec{B}$ , the vertical deflection $y$ of the proton on emerging from the magnetic region is approximately:

(A)

$3.20\times10^{-3}\ \mathrm{m}$

(B)

$3.20\times10^{-4}\ \mathrm{m}$

(C)

$6.40\times10^{-3}\ \mathrm{m}$

(D)

$3.20\times10^{-2}\ \mathrm{m}$

Q14. A long solid cylindrical conductor of radius $R$ carries a total current $I$ distributed so that the current density varies with radius as $J(r)=J_0\frac{r}{R}$ for $0\le r\le R$ (and $J=0$ for $r>R$ ). Using Ampère's law, the magnetic field at radial distance $r=\dfrac{R}{2}$ (inside the conductor) has magnitude and direction:

(A)

$\dfrac{\mu_0 I}{4\pi R}\,\hat{\phi}$

(B)

$\dfrac{\mu_0 I}{16\pi R}\,\hat{\phi}$

(C)

$\dfrac{\mu_0 I}{8\pi R}\,\hat{\phi}$

(D)

$\dfrac{\mu_0 I}{6\pi R}\,\hat{\phi}$

Q15. An alpha particle (mass $4u$ , charge $+2e$ ) and a deuteron (mass $2u$ , charge $+e$ ) are each accelerated from rest through the same potential difference $V$ and then enter a uniform magnetic field $B$ perpendicular to their velocities. If $r_\alpha$ and $r_D$ are their radii of curvature in the magnetic field, which statement is correct?

(A)

$r_\alpha = 2\,r_D$

(B)

$r_\alpha = \dfrac{r_D}{\sqrt{2}}$

(C)

$r_\alpha = \sqrt{2}\,r_D$

(D)

$r_\alpha = r_D$

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