A particle of charge q and mass m is moving along the x-axis with a velocity v and enters a region of electric field E and magnetic field B as shown in the figure below. For which figure the net force on the charge may be zero?

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Lorentz force
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A wire carrying a current i is placed in a uniform magnetic field in the form of the curve y=αsinπxL, 0x2L. The force acting on the wire is:

    

1. iBLπ                                        2. iBLπ

3. 2iBL                                        4. Zero

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Lorentz force
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If induction of magnetic field at a point is B and energy density is U, then which of the following graphs is correct?

1. 

2. 

3. 
4. 

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Magnetic field due to various cases
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 A long straight wire along the z-axis carries a current I in the negative z-direction. The magnetic field vector B at a point having coordinates (x, y) in the z = 0 plane is :

1. μ0I(yi^-xj^)2π(x2+y2)                 

2. μ0I(xi^+yj^)2π(x2+y2)

3. μ0I(xj^-yi^)2π(x2+y2)                 

4. μ0I(xi^-yj^)2π(x2+y2)

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Magnetic field due to various cases
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A circular coil is in y-z plane with centre at origin. The coil is carrying a constant current. Assuming direction of magnetic field at x = – 25 cm to be positive direction of magnetic field, which of the following graphs shows variation of magnetic field along x-axis

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Magnetic field due to various cases
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The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

(a) π242                             (b) π282

(c) π22                             (d) π42 

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Magnetic field due to various cases
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A particle of charge +q and mass m moving under the influence of a uniform electric field Ei^ and a uniform magnetic field Bk^ follows trajectory from P to Q as shown in figure. The velocities at P and Q are vi^ and -2vj^ respectively. Which of the following statement(s) is/are correct

          

(a) E=34mv2qa

(b) Rate of work done by electric field at P is 34mv3a

(c)  Rate of  work done by both fields at Q is zero

(d) All of the above

 

 

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Lorentz force
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Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming uniform wire is

                   

(a) 2μ0i3πa                                  (b) 2μ0i3πa

(c) 2μ0iπa                                   (d) 2μ0iπa   

Concept Questions :-

Magnetic field due to various cases
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For a positively charged particle moving in a  x- 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

(a)  E=0; B=bi^+ck^                 (b)  E=ai; B=ck^+ai^

(c) E=0;B=cj^+bk^                    (d)  E=ai;B=ck^+bj^

 

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Lorentz force
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Figure shows the cross-sectional view of the partially hollow cylindrical conductor with inner radius 'R' and outer radius '2R' carrying uniformly distributed current along it's axis. The magnetic induction at point 'P' at a distance 3R2 from the axis of the cylinder will be:

                     

1. Zero                               

2. 5μ0i72πR

3. 7μ0i18πR                             

4.  5μoi36πR

Concept Questions :-

Magnetic field due to various cases
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