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State
the definition of magnetic flux density. |
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The magnetic flux density B at a point is defined
as the force acting per unit length per unit current on a current-carrying
conductor perpendicular to the field lines at that point. |
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If a wire carries current I with length
l in a magnetic field is acted on by a magnetic force, the magnetic
flux density at right angles to the current is |
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Derive
an expression for the couple on a rectangular coil of n turns and dimensions
a ´ b
carrying a current I when placed in a uniform magnetic field of flux density
B at right angles to the sides of the coil of length a and at an angle
q to the sides
of length b. |
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The total magnetic force acting on each vertical edge is |
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These forces are equal but opposite. They form a couple
which is |
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where A = ab is the area of the coil. |
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| c. |
With
the aid of diagrams, describe the working of a moving-coil galvanometer
having a linear scale and suitable for measuring small currents. |
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When current flows in the coil, a torque is generated.
But it is restrained by a pair of hair-springs. The restoring couple depends
on the deflection: |
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where k is the torisional constant of
the springs. |
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The field is radial because the pole is curved
and a soft-iron cylinder is fixed at the center. Thus, the magnetic torque
is independent of the orientation of the coil. |
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Thus, the angle of deflection is directly proportional
to the current: |
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The scale is linear. |
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| d. |
What
do you understand about the current sensitivity of a galvanometer? The
coil of a galvanometer is to be made from a wire of a given length. For
the sake of high current sensitivity, explain whether more turns should
be wound so that each has a smaller area or less turns so that each has
a larger area. |
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Current sensitivity is the the angle of deflection per
unit current. |
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Give a wire of length 8d. The first arrangement (a) gives |
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The second arrangement (b) gives |
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Since the torque on a coil in a B-field is |
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The first arrangement gives a stronger torque
and thus a higher sensitivity. i.e. We should make less turns by increasing
the area of each turn. |
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| e. |
Explain
why the coil of a galvanometer is invariably wound on a light metal frame
instead of a plastic frame. |
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When a current is suddenly applied to the coil, it would
overshoot the equilibrium position (in the same way as releasing a mass
from a vertical spring). Then, the pointer would oscillate. |
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The oscillation can be damped if the coil is
wound on a light metal frame. As the coil moves, eddy current would be
induced to oppose the oscillatory motion. |
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