JEE Main & Advanced Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Question Bank

done Critical Thinking Total Questions - 26

• question_answer1)
  A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be \[\frac{1}{8}th\] to its value at the centre of the coil, is [MP PMT 1997]
  A)
             \[\frac{R}{\sqrt{3}}\]         done clear
  B)
             \[R\sqrt{3}\] done clear
  C)
             \[2\sqrt{3}\,R\]                    done clear
  D)
             \[\frac{2}{\sqrt{3}}R\] done clear
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• question_answer2)
  The field normal to the plane of a wire of n turns and radius r which carries a current i is measured on the axis of the coil at a small distance h from the centre of the coil. This is smaller than the field at the centre by the fraction
  A)
             \[\frac{3}{2}\frac{{{h}^{2}}}{{{r}^{2}}}\] done clear
  B)
             \[\frac{2}{3}\frac{{{h}^{2}}}{{{r}^{2}}}\] done clear
  C)
             \[\frac{3}{2}\frac{{{r}^{2}}}{{{h}^{2}}}\] done clear
  D)
             \[\frac{2}{3}\frac{{{r}^{2}}}{{{h}^{2}}}\] done clear
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• question_answer3)
  The magnetic field at the centre of a circular coil of radius r is \[\pi \] times that due to a long straight wire at a distance r from it, for equal currents. Figure here shows three cases : in all cases the circular part has radius r and straight ones are infinitely long. For same current the B field at the centre P in cases 1, 2, 3 have the ratio                                         [CPMT 1989]
  A)
             \[\left( -\frac{\pi }{2} \right):\left( \frac{\pi }{2} \right):\left( \frac{3\pi }{4}-\frac{1}{2} \right)\] done clear
  B)
             \[\left( -\frac{\pi }{2}+1 \right):\left( \frac{\pi }{2}+1 \right):\left( \frac{3\pi }{4}+\frac{1}{2} \right)\] done clear
  C)
             \[-\frac{\pi }{2}:\frac{\pi }{2}:3\frac{\pi }{4}\] done clear
  D)
             \[\left( -\frac{\pi }{2}-1 \right):\left( \frac{\pi }{2}-\frac{1}{4} \right):\left( \frac{3\pi }{4}+\frac{1}{2} \right)\] done clear
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• question_answer4)
  Two straight long conductors AOB and COD are perpendicular to each other and carry currents \[{{i}_{1}}\] and \[{{i}_{2}}\]. The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ACBD is                                                                          [MP PMT 1994]
  A)
             \[\frac{{{\mu }_{0}}}{2\pi a}({{i}_{1}}+{{i}_{2}})\]     done clear
  B)
             \[\frac{{{\mu }_{0}}}{2\pi a}({{i}_{1}}-{{i}_{2}})\] done clear
  C)
             \[\frac{{{\mu }_{0}}}{2\pi a}{{(I_{1}^{2}+I_{2}^{2})}^{1/2}}\]            done clear
  D)
             \[\frac{{{\mu }_{0}}}{2\pi a}\frac{{{I}_{1}}{{I}_{2}}}{({{I}_{1}}+{{I}_{2}})}\] done clear
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• question_answer5)
  A cell is connected between the points A and C of a circular conductor ABCD of centre O with angle A\[OC={{60}^{o}}\]. If \[{{B}_{1}}\] and \[{{B}_{2}}\] are the magnitudes of the magnetic fields at O due to the currents in ABC  and ADC  respectively, the ratio \[\frac{{{B}_{1}}}{{{B}_{2}}}\] is [KCET 1999; Pb PET 2000]
  A)
             0.2 done clear
  B)
             6 done clear
  C)
             1 done clear
  D)
             5 done clear
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• question_answer6)
  An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR The magnetic field due to this current at the point M is H1. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, The current in PQ remaining unchanged. The magnetic field at M is now \[{{H}_{2.}}\]The ratio \[{{H}_{1}}/{{H}_{2}}\] is given by   [IIT-JEE (Screening) 2000]
  A)
             \[\frac{1}{2}\] done clear
  B)
             1 done clear
  C)
             \[\frac{2}{3}\] done clear
  D)
             2 done clear
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• question_answer7)
  Two coaxial solenoids 1 and 2 of the same length are set so that one is inside the other. The number of turns per unit length are \[{{n}_{1}}\] and \[{{n}_{2}}\]. The currents \[{{i}_{1}}\] and \[{{i}_{2}}\] are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when                                        [Roorkee 2000]
  A)
             \[{{i}_{1}}\ne {{i}_{2}}\] and \[{{n}_{1}}={{n}_{2}}\] done clear
  B)
             \[{{i}_{1}}={{i}_{2}}\]and \[{{n}_{1}}\ne {{n}_{2}}\] done clear
  C)
             \[{{i}_{1}}={{i}_{2}}\] and \[{{n}_{1}}={{n}_{2}}\] done clear
  D)
             \[{{i}_{1}}{{n}_{1}}={{i}_{2}}{{n}_{2}}\] done clear
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• question_answer8)
  A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is                            [IIT-JEE (Screening) 2001]
  A)
             \[\frac{{{\mu }_{0}}NI}{b}\]   done clear
  B)
             \[\frac{2{{\mu }_{0}}NI}{a}\] done clear
  C)
             \[\frac{{{\mu }_{0}}NI}{2(b-a)}\ln \frac{b}{a}\]         done clear
  D)
             \[\frac{{{\mu }_{0}}{{I}^{N}}}{2(b-a)}\ln \frac{b}{a}\] done clear
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• question_answer9)
  A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P (a,0,a) points in the direction [IIT-JEE (Screening) 2001]
  A)
             \[\frac{1}{\sqrt{2}}(-\overset{{}}{\mathop{\hat{j}+\hat{k}}}\,)\] done clear
  B)
             \[\frac{1}{\sqrt{3}}(-\hat{j}+\hat{k}+\hat{i})\] done clear
  C)
             \[\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\]            done clear
  D)
             \[\frac{1}{\sqrt{2}}(\hat{i}+\hat{k})\] done clear
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• question_answer10)
  A long straight wire along the z-axis carries a current I in the negative z direction. The magnetic vector field \[\overset{\to }{\mathop{B}}\,\] at a point having coordinates (x, y)  in the z = 0 plane is  [IIT-JEE (Screening) 2002]
  A)
             \[\frac{{{\mu }_{o}}I\,(y\hat{i}-x\hat{j})}{2\pi ({{x}^{2}}+{{y}^{2}})}\]          done clear
  B)
             \[\frac{{{\mu }_{o}}I\,(x\hat{i}+y\hat{j})}{2\pi ({{x}^{2}}+{{y}^{2}})}\] done clear
  C)
             \[\frac{{{\mu }_{o}}I\,(x\hat{j}-y\hat{i})}{2\pi ({{x}^{2}}+{{y}^{2}})}\]          done clear
  D)
             \[\frac{{{\mu }_{o}}I\,(x\hat{i}-y\hat{j})}{2\pi ({{x}^{2}}+{{y}^{2}})}\] done clear
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• question_answer11)
  A particle of charge +q and mass m moving under the influence of a uniform electric field \[E\hat{i}\] and a uniform magnetic field \[B\hat{k}\] follows trajectory from P to Q as shown in figure. The velocities at P and Q are \[v\hat{i}\] and \[-2v\hat{j}\] respectively. Which of the following statement(s) is/are correct                                           [IIT 1991; BVP 2003]
  A)
             \[E=\frac{3}{4}\frac{m{{v}^{2}}}{qa}\] done clear
  B)
             Rate of work done by electric field at P is \[\frac{3}{4}\frac{m{{v}^{3}}}{a}\] done clear
  C)
             Rate of work done by electric field at P is zero done clear
  D)
             Rate of work done by both the fields at Q is zero done clear
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• question_answer12)
  \[{{H}^{+}},\,H{{e}^{+}}\] and \[{{O}^{++}}\] ions having same kinetic energy pass through a region of space filled with uniform magnetic field B directed perpendicular to the velocity of ions. The masses of the ions \[{{H}^{+}},\,H{{e}^{+}}\]and \[{{O}^{++}}\] are respectively in the ratio \[1:4:16\]. As a result
  A)
             \[{{H}^{+}}\] ions will be deflected most done clear
  B)
             \[{{O}^{++}}\] ions will be deflected least done clear
  C)
             \[H{{e}^{+}}\] and \[{{O}^{++}}\] ions will suffer same deflection done clear
  D)
             All ions will suffer the same deflection done clear
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• question_answer13)
  An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the +z direction, then  [IIT-JEE (Screening) 2000]
  A)
             Positive ions deflect towards +y direction and negative ions towards ?y direction done clear
  B)
             All ions deflect towards +y direction done clear
  C)
             All ions deflect towards ?y direction done clear
  D)
             Positive ions deflect towards ?y direction and negative ions towards +y direction done clear
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• question_answer14)
  An electron moves with speed \[2\times {{10}^{5}}\]m/s along the positive x-direction in the presence of a magnetic induction \[B=\hat{i}+4\hat{j}-3\hat{k}\](in Tesla.) The magnitude of the force experienced by the electron in Newton's is (charge on the electron =\[1.6\times {{10}^{-19}}C)\]                                            [EAMCET 2001]
  A)
             \[1.18\times {{10}^{-13}}\]     done clear
  B)
             \[1.28\times {{10}^{-13}}\] done clear
  C)
             \[1.6\times {{10}^{-13}}\]       done clear
  D)
             \[1.72\times {{10}^{-13}}\] done clear
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• question_answer15)
  A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from  x = a to x = b. The minimum value of v required so that the particle can just enter the region \[x>b\] is                       [IIT-JEE (Screening) 2002]
  A)
             \[qb\,B/m\]                          done clear
  B)
             \[q(b-a)B/m\] done clear
  C)
             \[qa\,B/m\]                           done clear
  D)
             \[q(b+a)B/2m\] done clear
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• question_answer16)
  For a positively charged particle moving in a  x-y­ plane initially along the x-axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond P. The curved path is shown in the x-y plane and is found to be non-circular. Which one of the following combinations is possible                 [IIT-JEE (Screening) 2003]
  A)
             \[\overrightarrow{E}=0;\,\overrightarrow{B}=b\hat{i}\,+c\hat{k}\]              done clear
  B)
             \[\overrightarrow{E}=ai;\,\overrightarrow{B}=c\hat{k}\,+a\hat{i}\] done clear
  C)
             \[\overrightarrow{E}=0;\,\overrightarrow{B}=c\hat{j}\,+b\hat{k}\]              done clear
  D)
             \[\overrightarrow{E}=ai;\,\overrightarrow{B}=c\hat{k}\,+b\hat{j}\] done clear
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• question_answer17)
   A horizontal rod of mass 10 gm and length 10 cm is placed on a smooth plane inclined at an angle of \[60{}^\circ \] with the horizontal, with the length of the rod parallel to the edge of the inclined plane. A uniform magnetic field of induction B is applied vertically downwards. If the current through the rod is 1.73 ampere, then the value of B for which the rod remains stationary on the inclined plane is
  A)
             1.73 Tesla                               done clear
  B)
             \[\frac{1}{1.73}\] Tesla done clear
  C)
             1 Tesla                                     done clear
  D)
             None of the above done clear
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• question_answer18)
  Two long wires are hanging freely. They are joined first in parallel and then in series and then are connected with a battery. In both cases, which type of force acts between the two wires                                                 [MP PET 1993]
  A)
             Attraction force when in parallel and repulsion force when in series done clear
  B)
             Repulsion force when in parallel and attraction force when in series done clear
  C)
             Repulsion force in both cases done clear
  D)
             Attraction force in both cases done clear
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• question_answer19)
  A wire of length L metre carrying a current of I ampere is bent in the form of a circle. Its magnitude of magnetic moment will be      [MP PET 1995; MH CET 2004]
  A)
             \[\frac{IL}{4\pi }\]               done clear
  B)
             \[\frac{I{{L}^{2}}}{4\pi }\] done clear
  C)
             \[\frac{{{I}^{2}}{{L}^{2}}}{4\pi }\]                                     done clear
  D)
             \[\frac{{{I}^{2}}L}{4\pi }\] done clear
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• question_answer20)
  A thin circular wire carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment             [MP PET 2003; MP PMT 2004]
  A)
             M   done clear
  B)
             \[\frac{4}{{{\pi }^{2}}}M\] done clear
  C)
             \[\frac{4}{\pi }M\]              done clear
  D)
             \[\frac{\pi }{4}M\] done clear
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• question_answer21)
  A particle of charge q and mass m moves in a circular orbit of radius r with angular speed \[\omega \]. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on                            [IIT-JEE (Screening) 2000]
  A)
             \[\omega \,\text{and}\,q\]    done clear
  B)
             \[\omega \,\,q\,\text{and}\,m\] done clear
  C)
             \[q\,\,\text{and}\,m\]      done clear
  D)
             \[\omega \,\text{and}\,m\] done clear
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• question_answer22)
  An elastic circular wire of length l carries a current I. It is placed in a uniform magnetic field \[\overset{\to }{\mathop{B}}\,\] (Out of paper) such that its plane is perpendicular to the direction of \[\overset{\to }{\mathop{B}}\,\]. The wire will experience                                                        [MP PET 2000]
  A)
             No force                                 done clear
  B)
             A stretching force done clear
  C)
             A compressive force          done clear
  D)
             A torque done clear
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• question_answer23)
  A and B are two conductors carrying a current i in the same direction. x and y are two electron beams moving in the same direction                              [Karnataka CET (Engg./Med.) 2002]
  A)
             There will be repulsion between A and B attraction between x and y done clear
  B)
             There will be attraction between A and B, repulsion between x and y done clear
  C)
             There will be repulsion between A and B and also x and y  done clear
  D)
             There will be attraction between A and B and also x and y done clear
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• question_answer24)
  Wires 1 and 2 carrying currents \[{{i}_{1}}\] and \[{{i}_{2}}\]respectively are inclined at an angle \[\theta \] to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire1 [AIEEE 2002]
  A)
             \[\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}\,{{i}_{2}}\,dl\,\tan \theta \]    done clear
  B)
             \[\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}\,{{i}_{2}}\,dl\,\sin \theta \] done clear
  C)
             \[\frac{{{\mu }_{0}}}{2\pi r}{{i}_{1}}\,{{i}_{2}}\,dl\,\cos \theta \] done clear
  D)
             \[\frac{{{\mu }_{0}}}{4\pi r}{{i}_{1}}\,{{i}_{2}}\,dl\,\sin \theta \] done clear
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• question_answer25)
  A conducting loop carrying a current I is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to    [IIT-JEE (Screening) 2003]
  A)
             Contract                                  done clear
  B)
             Expand done clear
  C)
             Move towards +ve x -axis done clear
  D)
             Move towards ?ve x-axis done clear
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• question_answer26)
  A current carrying loop is placed in a uniform magnetic field in four different orientations, I,II, III & IV arrange them in the decreasing order of potential Energy [IIT-JEE (Screening) 2003] I.                          II. III.                                 IV.
  A)
             I > III > II > IV                         done clear
  B)
             I > II >III > IV done clear
  C)
             I > IV > II > III                         done clear
  D)
             III > IV > I > II done clear
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