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

Magnitude of flux of the flat coil, $ϕ_{1} = B . A .$

$Flux, ϕ_{2} = 0 (Outside the coil)$

Induced emf in the magnet, $E = - N . \frac{dϕ}{dt}$
This implies, $I . R = - N \frac{(ϕ_{2} - ϕ_{1})}{(t_{2} - t_{1})}$
$\frac{q}{t} R = - N \frac{(0 - B . A)}{t}$
That is,
$qR = + NBA B = \frac{qR}{NA} = \frac{7.5 \times 10^{- 3} \times . 50}{25 \times 2 \times 10^{- 4}} = \frac{75 \times 25 \times 10^{- 3 + 4}}{25 \times 2 \times 1000}$

$= - 75 \times 10^{1 - 3} = 0.75 Webr / m^{2} .$

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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