A proton of mass 1.67×10-27kg and charge 1.6×10-19C is projected with a speed of 2×106m/s at an angle of 60° to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along Y-axis, the path of the proton is:

1. A circle of radius = 0.2 m and time period π×10-7s

2. A circle of radius = 0.1 m and time period 2π×10-7s 

3. A helix of radius = 0.1 m and time period 2π×10-7s

4. A helix of radius = 0.2 m and time period 4π×10-7s

Concept Questions :-

Lorentz force
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The magnetic field at the centre of a circular coil of radius r is π 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

  

(a) -π2:π2 :3π4-12

(b) -π2+1:π2+1:3π4+12

(c) -π2:π2:3π4

(d) -π2-1:π2-14:3π4+12

Concept Questions :-

Magnetic field due to various cases
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A proton and a deuteron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For the motion of proton and deuteron on a circular path of radius Rpand Rd respectively, the correct statement is:


(a) Rd=2Rp            (b) Rd=Rp/2

(c) Rd=Rp                  (d) Rd=2Rp

 

Concept Questions :-

Lorentz force
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Two straight long conductors AOB and COD are perpendicular to each other and carry currents i1 and i2 . 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: 

1. μ02πa(i1+i2)                    2. μ02πa(i1-i2)

3. μ02πai12+i221/2                4. μ02πai1i2(i1+i2)

Concept Questions :-

Magnetic field due to various cases
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The charge on a particle Y is double the charge on particle X. These two particles X and Y after being accelerated through the same potential difference enter a region of the uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of the mass of X to that of Y is:

(a) 2R1R22                      (b) R12R22

(c)  R122R22                           (d) 2R1R2 

Concept Questions :-

Lorentz force
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In the given figure, the electron enters into the magnetic field. It deflects in ...... direction

                      

(a) + ve X direction

(b) – ve X direction

(c) + ve Y direction

(d) – ve Y direction

Concept Questions :-

Lorentz force
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A cell is connected between the points A and C of a circular conductor ABCD of centre O with angle AOC = 60° . If B1 and B2 are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, the ratio B1B2 is:

1. 0.2                             

2. 6                                    

3. 1

4. 5                    

 

Concept Questions :-

Magnetic field due to various cases
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An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively Re, RpRd and Rα. It follows that 

(a) Re=Rp                (b) Rp=Rd

(c) Rd=Rα                 (d) Rp=Rα

Concept Questions :-

Lorentz force
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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 H2The ratio H1/H2 is given by

(a) 12                                                

(b)  1

(c)  23

(d)  2

Concept Questions :-

Magnetic field due to various cases
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A very long straight wire carries a current I. At the instant when a charge +O~ at point P has velocity v , as shown, the force on the charge is:

1. Opposite to OX                            2. Along OX

3. Opposite to OY                             4. Along OY

Concept Questions :-

Lorentz force
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