Physics-
General
Easy

Question

If the magnetic field at 'P' in the given figure can be written as K tan open parentheses fraction numerator alpha over denominator 2 end fraction close parentheses then K is

  1. fraction numerator mu subscript 0 end subscript I over denominator 4 pi d end fraction    
  2. fraction numerator mu subscript 0 end subscript I over denominator 2 pi d end fraction    
  3. fraction numerator mu subscript 0 end subscript I over denominator pi d end fraction    
  4. fraction numerator 2 mu subscript 0 end subscript I over denominator pi d end fraction    

The correct answer is: fraction numerator mu subscript 0 end subscript I over denominator 2 pi d end fraction


    Let us compute the magnetic field due to any one segment :

    table row cell B equals fraction numerator mu subscript 0 end subscript i over denominator 4 pi left parenthesis d s i n invisible function application alpha right parenthesis end fraction open parentheses c o s invisible function application 0 to the power of 6 end exponent plus c o s invisible function application left parenthesis 180 minus alpha right parenthesis close parentheses end cell row cell equals fraction numerator mu subscript 0 end subscript i over denominator 4 pi left parenthesis d s i n invisible function application alpha right parenthesis end fraction left parenthesis 1 minus c o s invisible function application alpha right parenthesis equals fraction numerator mu subscript 0 end subscript i over denominator 4 pi d end fraction t a n invisible function application fraction numerator alpha over denominator 2 end fraction end cell row cell text end text text R end text text e end text text s end text text u end text text l end text text t end text text a end text text n end text text t end text text end text text f end text text i end text text e end text text l end text text d end text text end text text w end text text i end text text l end text text l end text text end text text b end text text e end text text : end text text end text end cell row cell B subscript n c t end subscript equals 2 B equals fraction numerator mu subscript 0 end subscript i over denominator 2 pi d end fraction t a n invisible function application fraction numerator alpha over denominator 2 end fraction rightwards double arrow k equals fraction numerator mu subscript 0 end subscript i over denominator 2 pi d end fraction end cell end table

    Related Questions to study

    General
    physics-

    In the figure shown ABCDEFA was a square loop of side l , but is folded in two equal parts so that half of it lies in xz plane and the other half lies in the yz plane. The origin 'O' is centre of the frame also. The loop carries current ' i '. The magnetic field at the centre is:

    In the figure shown ABCDEFA was a square loop of side l , but is folded in two equal parts so that half of it lies in xz plane and the other half lies in the yz plane. The origin 'O' is centre of the frame also. The loop carries current ' i '. The magnetic field at the centre is:

    physics-General
    General
    physics-

    The negatively and uniformly charged nonconducting disc as shown in the figure is rotated clockwise with great angular speed. The direction of the magnetic field at point A in the plane of the disc is

    The negatively and uniformly charged nonconducting disc as shown in the figure is rotated clockwise with great angular speed. The direction of the magnetic field at point A in the plane of the disc is

    physics-General
    General
    physics-

    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).

    physics-General
    parallel
    General
    physics-

    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 the same material. Their lengths are the same, widths are w subscript 1 end subscript and w subscript 2 end subscript and thicknesses are d subscript 1 end subscript and d subscript 2 end subscript , respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V subscript 1 end subscript and V subscript 2 end subscript are the potential differences between K and M in strips 1 and 2 , respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(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 the same material. Their lengths are the same, widths are w subscript 1 end subscript and w subscript 2 end subscript and thicknesses are d subscript 1 end subscript and d subscript 2 end subscript , respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V subscript 1 end subscript and V subscript 2 end subscript are the potential differences between K and M in strips 1 and 2 , respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is (are).

    physics-General
    General
    physics-

    In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B subscript 1 end subscript (sold line) and B subscript 2 end subscript (dashed line). If B subscript 2 s end subscript is larger than B subscript 1 end subscript , which of the following graphs shows the correct variation of R with T in these fields? Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T subscript C end subscript (0). An interesting property of superconductors is that their critical temperature becomes smaller than T subscript C end subscript (0) if they are placed in a magnetic field, i.e., the critical temperature T subscript C end subscript (B) is a function of the magnetic field strength B. The dependence of T subscript C end subscript (B) on B is shown in the figure.

    A superconductor has T subscript C end subscript (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its T subscript C end subscript decreases to 75 K. For this material one can definitely say that when

    In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B subscript 1 end subscript (sold line) and B subscript 2 end subscript (dashed line). If B subscript 2 s end subscript is larger than B subscript 1 end subscript , which of the following graphs shows the correct variation of R with T in these fields? Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T subscript C end subscript (0). An interesting property of superconductors is that their critical temperature becomes smaller than T subscript C end subscript (0) if they are placed in a magnetic field, i.e., the critical temperature T subscript C end subscript (B) is a function of the magnetic field strength B. The dependence of T subscript C end subscript (B) on B is shown in the figure.

    A superconductor has T subscript C end subscript (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its T subscript C end subscript decreases to 75 K. For this material one can definitely say that when

    physics-General
    General
    physics-

    In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B subscript 1 end subscript (sold line) and B subscript 2 end subscript (dashed line). If B subscript 2 s end subscript is larger than B subscript 1 end subscript , which of the following graphs shows the correct variation of R with T in these fields? Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T subscript C end subscript (0). An interesting property of superconductors is that their critical temperature becomes smaller than T subscript C end subscript (0) if they are placed in a magnetic field, i.e., the critical temperature T subscript C end subscript (B) is a function of the magnetic field strength B. The dependence of T subscript C end subscript (B) on B is shown in the figure.

    In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B subscript 1 end subscript (sold line) and B subscript 2 end subscript (dashed line). If B subscript 2 end subscript is larger than B subscript 1 end subscript , which of the following graphs shows the correct variation of R with T in these fields?

    In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B subscript 1 end subscript (sold line) and B subscript 2 end subscript (dashed line). If B subscript 2 s end subscript is larger than B subscript 1 end subscript , which of the following graphs shows the correct variation of R with T in these fields? Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T subscript C end subscript (0). An interesting property of superconductors is that their critical temperature becomes smaller than T subscript C end subscript (0) if they are placed in a magnetic field, i.e., the critical temperature T subscript C end subscript (B) is a function of the magnetic field strength B. The dependence of T subscript C end subscript (B) on B is shown in the figure.

    In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B subscript 1 end subscript (sold line) and B subscript 2 end subscript (dashed line). If B subscript 2 end subscript is larger than B subscript 1 end subscript , which of the following graphs shows the correct variation of R with T in these fields?

    physics-General
    parallel
    General
    physics-

    A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is :

    A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is :

    physics-General
    General
    physics-

    A magnetic field stack B with rightwards arrow on top equals B subscript 0 end subscript stack j with rightwards arrow on top exists in the region a less than x less than 2 a and stack B with rightwards arrow on top equals negative B subscript 0 end subscript stack j with bar on top in the region 2 a less than x less than 3 a, where B subscript 0 end subscript is a positive constant. A positive point charge moving with a velocity stack v with rightwards arrow on top equals v subscript 0 end subscript stack i with bar on top where V subscript 0 end subscript is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like

    A magnetic field stack B with rightwards arrow on top equals B subscript 0 end subscript stack j with rightwards arrow on top exists in the region a less than x less than 2 a and stack B with rightwards arrow on top equals negative B subscript 0 end subscript stack j with bar on top in the region 2 a less than x less than 3 a, where B subscript 0 end subscript is a positive constant. A positive point charge moving with a velocity stack v with rightwards arrow on top equals v subscript 0 end subscript stack i with bar on top where V subscript 0 end subscript is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like

    physics-General
    General
    physics-

    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 :

    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 :

    physics-General
    parallel
    General
    physics-

    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

    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

    physics-General
    General
    physics-

    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

    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

    physics-General
    General
    physics-

    For a positively charged particle moving in a x – y plane initially along the x–axis, there is a sudden change in it path due to the presence of electric and/or magnetic field 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?

    For a positively charged particle moving in a x – y plane initially along the x–axis, there is a sudden change in it path due to the presence of electric and/or magnetic field 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?

    physics-General
    parallel
    General
    physics-

    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

    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

    physics-General
    General
    physics-

    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

    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

    physics-General
    General
    physics-

    An infinitely long conductor PQR is bent to form a right angle as shown in figure. A current I flows through PQR. The magnetic field due to this current at the point M is H subscript 1 end subscript . Now, another infinitely long straight conductor QS is connected at Q, so that 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 subscript 2 end subscript . The ratio H subscript 1 end subscript /H subscript 2 end subscript is given by :

    An infinitely long conductor PQR is bent to form a right angle as shown in figure. A current I flows through PQR. The magnetic field due to this current at the point M is H subscript 1 end subscript . Now, another infinitely long straight conductor QS is connected at Q, so that 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 subscript 2 end subscript . The ratio H subscript 1 end subscript /H subscript 2 end subscript is given by :

    physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.