Physics-
General
Easy

Question

A uniform, constant magnetic field stack B with bar on top is directed at an angle of 45 to the power of ring operator end exponent to the x-axis in the xy-plane, PQRS is a rigid square wire frame carrying a steady current I subscript 0 end subscript, with its centre at the origin O. At time t = 0, the frame is at rest in the position shown in the figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L.. The torque stack tau with rightwards arrow on top about O acting on the frame due to the magnetic field will be

  1. stack tau with rightwards arrow on top equals fraction numerator B I subscript 0 end subscript L to the power of 2 end exponent over denominator square root of 2 end fraction left parenthesis negative stack i with hat on top plus stack j with hat on top right parenthesis    
  2. stack tau with rightwards arrow on top equals fraction numerator B I subscript 0 end subscript L to the power of 2 end exponent over denominator square root of 2 end fraction left parenthesis stack i with hat on top minus j right parenthesis    
  3. stack tau with rightwards arrow on top equals fraction numerator B I subscript 0 end subscript L to the power of 2 end exponent over denominator square root of 2 end fraction left parenthesis stack i with hat on top plus stack j with hat on top right parenthesis    
  4. stack tau with rightwards arrow on top equals fraction numerator B I subscript 0 end subscript L to the power of 2 end exponent over denominator square root of 2 end fraction left parenthesis negative stack i with hat on top minus stack j with hat on top right parenthesis    

The correct answer is: stack tau with rightwards arrow on top equals fraction numerator B I subscript 0 end subscript L to the power of 2 end exponent over denominator square root of 2 end fraction left parenthesis negative stack i with hat on top plus stack j with hat on top right parenthesis


    tau equals stack m with rightwards arrow on top cross times stack B with rightwards arrow on top S equals I subscript 0 end subscript L to the power of 2 end exponent stack k with hat on top cross times open parentheses fraction numerator B over denominator square root of 2 end fraction stack i with hat on top plus fraction numerator B over denominator square root of 2 end fraction stack j with hat on top close parentheses equals fraction numerator I subscript 0 end subscript L to the power of 2 end exponent B over denominator square root of 2 end fraction left parenthesis stack j with rightwards arrow on top minus stack i with hat on top right parenthesis

    Related Questions to study

    General
    physics-

    In the plane mirror, the co-ordinates of image of charged particle (initially at origin as shown) after two and half time periods are (initial velocity V0 is in the xy-plane and the plane mirror is perpendicular to the x-axis. A uniform magnetic field text end text text Bî end text exists in the whole space. P o is pitch of helix, R subscript 0 end subscript is radius of helix).

    In the plane mirror, the co-ordinates of image of charged particle (initially at origin as shown) after two and half time periods are (initial velocity V0 is in the xy-plane and the plane mirror is perpendicular to the x-axis. A uniform magnetic field text end text text Bî end text exists in the whole space. P o is pitch of helix, R subscript 0 end subscript is radius of helix).

    physics-General
    General
    physics-

    A uniform magnetic field of magnitude 1 T exists in region y greater or equal than 0 is along stack k with hat on top direction as shown. A particle of charge 1 C is projected from point left parenthesis negative square root of 3 comma negative 1 right parenthesis towards origin with speed 1 m/sec. If mass of particle is 1 kg, then co-ordinates of centre of circle in which particle moves are

    A uniform magnetic field of magnitude 1 T exists in region y greater or equal than 0 is along stack k with hat on top direction as shown. A particle of charge 1 C is projected from point left parenthesis negative square root of 3 comma negative 1 right parenthesis towards origin with speed 1 m/sec. If mass of particle is 1 kg, then co-ordinates of centre of circle in which particle moves are

    physics-General
    General
    physics-

    Figure shows an equilateral triangle ABC of side lambda carrying currents, placed in uniform magnetic field B. The magnitude of magnetic force on triangle is

    Figure shows an equilateral triangle ABC of side lambda carrying currents, placed in uniform magnetic field B. The magnitude of magnetic force on triangle is

    physics-General
    parallel
    General
    physics-

    If a charged particle of charge to mass ratio q/m = alpha is entering in a uniform magnetic field of strength B which is extended up to 4d as shown in figure at a speed v = (2alphad)(B), then which of the following is correct :

    If a charged particle of charge to mass ratio q/m = alpha is entering in a uniform magnetic field of strength B which is extended up to 4d as shown in figure at a speed v = (2alphad)(B), then which of the following is correct :

    physics-General
    General
    physics-

    An electron moving with velocity V along the axis approaches a circular current carrying loop as shown in the figure. The magnitude of magnetic force on electron at this instant is

    An electron moving with velocity V along the axis approaches a circular current carrying loop as shown in the figure. The magnitude of magnetic force on electron at this instant is

    physics-General
    General
    physics-

    A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius R1 & the outer conductor is hollow of inner radius R2 and outer radius R3. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as:

    A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius R1 & the outer conductor is hollow of inner radius R2 and outer radius R3. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as:

    physics-General
    parallel
    General
    physics-

    Figure shows an amperian path ABCDA. Part ABC is in vertical plane PSTU while part CDA is in horizontal plane PQRS. Direction of circulation along the path is shown by an arrow near point B and at text D.  end text integral stack B with rightwards arrow on top times stack d with rightwards arrow on top l for this path according to Ampere’s law will be :

    Figure shows an amperian path ABCDA. Part ABC is in vertical plane PSTU while part CDA is in horizontal plane PQRS. Direction of circulation along the path is shown by an arrow near point B and at text D.  end text integral stack B with rightwards arrow on top times stack d with rightwards arrow on top l for this path according to Ampere’s law will be :

    physics-General
    General
    physics-

    A steady current is set up in a cubic network composed of wires of equal resistance and length d as shown in figure. What is the magnetic field at the centre of cube P due to the cubic network ?

    A steady current is set up in a cubic network composed of wires of equal resistance and length d as shown in figure. What is the magnetic field at the centre of cube P due to the cubic network ?

    physics-General
    General
    physics-

    Two infinitely long linear conductors are arranged perpendicular to each other and are in mutually perpendicular planes as shown in figure. If I subscript 1 end subscript equals 2 A along the y-axis and I subscript 2 end subscript equals 3 A along negative z-axis and AP = AB = 1 cm. The value of magnetic field strength

    Two infinitely long linear conductors are arranged perpendicular to each other and are in mutually perpendicular planes as shown in figure. If I subscript 1 end subscript equals 2 A along the y-axis and I subscript 2 end subscript equals 3 A along negative z-axis and AP = AB = 1 cm. The value of magnetic field strength

    physics-General
    parallel
    General
    physics-

    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

    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

    physics-General
    General
    physics-

    The magnetic field at the origin due to the current flowing in the wire as shown in figure below is

    The magnetic field at the origin due to the current flowing in the wire as shown in figure below is

    physics-General
    General
    physics-

    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

    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

    physics-General
    parallel
    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

    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.