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प्रश्न
It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm2 with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction. The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 Ω. Estimate the field strength of magnet.
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उत्तर
Area of the small flat search coil, A = 2 cm2 = 2 × 10−4 m2
Number of turns on the coil, N = 25
Total charge flowing in the coil, Q = 7.5 mC = 7.5 × 10−3 C
Total resistance of the coil and galvanometer, R = 0.50 Ω
Induced current in the coil,
I = `("Induced emf (e)")/"R"` ...............(1)
Induced emf is given as:
e = `-"N"("d"phi)/("dt")` ..............(2)
Where,
`"d"phi` = Charge in flux
Combining equations (1) and (2), we get
I = `-("N"("d"phi)/("dt"))/("R")`
Idt = `-"N"/"R" "d"phi` ...........(3)
Initial flux through the coil, `phi_"i"` = BA
Where,
B = Magnetic field strength
Final flux through the coil, `phi_"f"` = 0
Integrating equation (3) on both sides, we have
`int"Idt" = -"N"/"R"int_(phi_"i")^(phi_"f")"d"phi`
But total Charge Q = `int"Idt"`
∴ Q = `-"N"/"R"(phi_"f" - phi_"i") = -"N"/"R"(-phi_"i") = +("N"phi_"i")/"R"`
Q = `("NBA")/"R"`
∴ B = `("QR")/("NA")`
= `(7.5 xx 10^-3 xx 0.5)/(25 xx 2 xx 10^-4)`
= 0.75 T
Hence, the field strength of the magnet is 0.75 T.
संबंधित प्रश्न
State whether the following statement are true or false:
A generator works on the principle of electromagnetic induction.
An induced current is produced when a magnet is moved into a coil. The magnitude of induced current does not depend on:
(a) the speed with which the magnet is moved
(b) the number of turns of the coil
(c) the resistivity of the wire of the coil
(d) the strength of the magnet
In which of the following case does the electromagnetic induction occur?
A loop of wire is held near a magnet.
Electromagnetic induction means ______.
Consider the energy density in a solenoid at its centre and that near its ends. Which of the two is greater?
L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?
(a) `1/(RC)`
(b) `R/L`
(c) `1/sqrt(LC)`
(d) C/L
Fig. shows a simple form of an A.C. generator.
(a) Name the parts labeled A and B.
(b) What would be the effect of doubling the number of turns on the coil if the speed of rotation remains unchanged?
(c) Which of the output terminals is positive if the coil is rotating in the
direction shown in the diagram (anticlockwise)?
( d ) What is the position of the rotating coil when p.d. across its ends is zero? Explain why p.d. is zero when the coil is at this position .
(e) Sketch a graph showing how the p.d. across the ends of the rotating coil varies with time for an A.C. dynamo.
( f) On th e same sheet of paper and vertically below the first graph using the same time scale, sketch graphs to show the effect of
(i) Doubling the speed of rotation and at the same time keeping
the field and the number of turns constant,
(ii ) Doubling the number of turns on the coil and at the same time
doubling the speed of rotation of the coil, keeping th e speed
constant.
A coil has a self-inductance of 0·05 Henry. Find the magnitude of the emf induced in it when the current flowing through it is changing at the rate of 100 As-1.
State Fleming’s Right Hand Rule.
Which of the following scientist invented the rule of electromagnetic induction?
Write the two names in the following diagram.
Right hand thumb rule.
An induced current of 2.5 mA flows through a single conductor of resistance 100 Ω. Find out the rate at which the magnetic flux is cut by the conductor.
A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 x 10-5 Wb, find the magnetic energy stored in the medium surrounding the coil.
Shown in the figure below is a metre bridge set up with null deflection in the galvanometer. The value of the unknown resistance R is ______
Metal rings P and Q are lying in the same plane, where current I is increasing steadily. The induced current in metal rings is shown correctly in figure.
The instrument that use to defect electric current in the circuit is known as ____________.
Ansari Sir was demonstrating an experiment in his class with the setup as shown in the figure below.
A magnet is attached to a spring. The magnet can go in and out of the stationary coil. He lifted the Magnet and released it to make it oscillate through the coil.
Based on your understanding of the phenomenon, answer the following question.
What is the principle which Ansari Sir is trying to demonstrate?
Name some equipment that uses electromagnetism for functioning.
