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Lorentz force

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A magnetic field B = B_(0) (y//a)(hat)k is into the paper in the +z direction, B_(0) and a are positive constants. A square loop EFGH of side a, mass m and resistance R, in x-y plane, starts falling under the influence of gravity see figure. Note the direction of x and y axis in figure. Find (a) the induced current in the loop and indicate its direction. (b) the total Lorentz force acting on the loop and indicate its direction, and (c) an expression for the speed of the loop, v(t) and its terminal value.

(a) A rod of length is moved horizontally with a uniform velocity 'v' in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the exprwession for the emf induced across the ends of the rod. (b) How does one understand this motional emf by invoking the Lorentz force on the free charge carries of the condutor ? Explain.

Knowledge Check

  • A proton is moving with a velocity of 5 xx 10^(5) m//s along the Y-direction. It is acted upon by an electric field of intensity 10^(5) V/m along the X-direction and a magnetic field of 1 Wb//m^(2) along the Z-direction. Then the Lorentz force on the particle is :

    A
    zero
    B
    `8.0 xx 10^(-4)` N along X-axis
    C
    `9.6 xx 10^(-14)` along Z-axis
    D
    `9.6 xx 10^(-14)` along X-axis

  • A magnetic field B = (B_0 y//a) hatk is acting into the paper in the + z direction. Bo and a are positive constants. A square loop EFGH of side a, mass m and resistance R kept in x-y plane starts falling under the influence of gravity. Note the directions of x and y in the figure. Find the total Lorentz force acting on the loop and indicate its direction.

    A
    `vecF = (B_0^2 a^2 v)/(R) hatj` upwards
    B
    `vecF = (B_0^2 a^2 v)/(R) hatj` downwards
    C
    `vecF = (B_0^2 a^2 v)/(R) hatj` upwards
    D
    `vecF = (B_0^2 a^2 v)/(R) hatj` downwards

  • Which of the following are contact forces ? A. Friction B. Gravitational force C. Magnetic force D. Muscular force

    A
    A and B
    B
    B and C
    C
    A and D
    D
    B and D

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    A clock moves along an x axis at a speed of 0.700c and reads zero as it passes the origin of the axis. (a) Calculate the clock's Lorentz factor. (b) What time does the clock read as it passes x = 180m ?

    Gravitational force is a weak force but still it is considered the most important force. Why ?

    Which of the following are non - contact forces ? Magnetic force, Frictional force, Gravitional force, Muscular force, Electrostatic force.

    Gravitational force is the strongest force in nature

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