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An infinitely long wire carrying current I is along Y axis such that its one end is at point A (0, b) while the wire extends up to + infinity. The magnitude of magnetic field strength at point (a, 0) is

  1. fraction numerator mu subscript 0 end subscript I over denominator 4 pi a end fraction open parentheses 1 plus fraction numerator b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction close parentheses    
  2. fraction numerator mu subscript 0 end subscript I over denominator 4 pi a end fraction open parentheses 1 minus fraction numerator b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction close parentheses    
  3. fraction numerator mu subscript 0 end subscript I over denominator 4 pi a end fraction open parentheses fraction numerator b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction close parentheses    
  4. None of these    

The correct answer is: fraction numerator mu subscript 0 end subscript I over denominator 4 pi a end fraction open parentheses 1 minus fraction numerator b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction close parentheses

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In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively. A uniform magnetic field B rho is applied on the strip along the positive y-direction. Due to this, the charge carries experience a net deflection along the z-direction. This results in accumulation of charge caries on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n subscript 1 end subscript and n subscript 2 end subscript , respectively. Strip 1 is placed in magnetic field B subscript 1 end subscript and strip 2 is placed in magnetic field B subscript 2 end subscript , both along positive y-directions. Then V subscript 1 end subscript and V subscript 2 end subscript are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option (S) is (are).

In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively. A uniform magnetic field B rho is applied on the strip along the positive y-direction. Due to this, the charge carries experience a net deflection along the z-direction. This results in accumulation of charge caries on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n subscript 1 end subscript and n subscript 2 end subscript , respectively. Strip 1 is placed in magnetic field B subscript 1 end subscript and strip 2 is placed in magnetic field B subscript 2 end subscript , both along positive y-directions. Then V subscript 1 end subscript and V subscript 2 end subscript are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option (S) is (are).

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An electron moving with a speed u along the positive x–axis at y = 0 enters a region of uniform magnetic field stack B with bar on top equals negative B subscript 0 end subscript stack k with bar on top which exists to the right of y–axis. The electron exist from the region after some time with the speed v at co–ordinate y, then :

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Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are v subscript A end subscript and v subscript B end subscript respectively and the trajectories are as shown in the figure. Then

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