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Derive the equation relating the total charge Q that flows through a search coil (Conceptual Example 29.3) to the magnetic-field magnitude B. The search coil has N turns, each with area A, and the flux through the coil is decreased from its initial maximum value to zero in a time Δt. The resistance of the coil is R, and the total charge is Q=IΔt, where I is the average current induced by the change in flux.

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Answer:

Q= NBA/R

Explanation:

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Cricetus

The equation relating the total charge, magnitude, turns, time will be "[tex]\frac{NBA}{R}[/tex]".

Magnetic field

According to the question,

Resistance = R

Total charge = Q

Current = I

Number of turns = N

Time = Δt

and,

Q = IΔt ...(equation 1)

We know the flux,

→ [tex]\Phi[/tex] = NBA

Emf induced,

   ε = [tex]\frac{- \Delta \Phi}{\Delta t}[/tex]

Δ[tex]\Phi[/tex] = [tex]\Phi_2 - \Phi_1[/tex]

then,

   ε = [tex]\frac{NBA}{\Delta t}[/tex]

As we know, Voltage (V) = iR

then, ε = [tex]\frac{NBA}{\Delta t}[/tex] = iR

         i = [tex]\frac{NBA}{R \Delta t}[/tex]

Hence, by applying the values in "equation 1"    

→ Q = iΔt

      = [tex]\frac{NBA}{R \Delta t}[/tex] × Δt

      = [tex]\frac{NBA}{R}[/tex]

Thus the response above is correct.

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