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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

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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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