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# 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 Cm^2 With 25 Closely Wound Turns, is Positioned Normal to the Field Direction, and Then Quickly Snatched Out of the Field Region - CBSE (Science) Class 12 - Physics

#### Question

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.

#### Solution

Area of the small flat search coil, A = 2 cm= 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(dphi)/(dt)    ...(2)

Where,

dphi = Charge in flux

Combining equations (1) and (2), we get

I=-(N(dphi)/(dt))/(R)

Idt=-N/Rdphi

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

intIdt=-N/Rint_(phi_i)^(phi_f)dphi

But total Charge Q=intIdt

therefore Q=-N/R(phi_f-phi_i)=-N/R(-phi_i)=+(Nphi_i)/R

Q=(NBA)/R

therefore B=(QR)/(NA)

=(7.5xx10^-3xx0.5)/(25xx2xx10^-4)=0.75 T

Hence, the field strength of the magnet is 0.75 T.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 6: Electromagnetic Induction
Q: 13 | Page no. 231

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Solution 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 Cm^2 With 25 Closely Wound Turns, is Positioned Normal to the Field Direction, and Then Quickly Snatched Out of the Field Region Concept: Electromagnetic Induction.
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