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One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area 5.87 × 10-3 m2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 14.9 Ω. If an externally applied uniform longitudinal magnetic field in the core changes from 1.93 T in one direction to 1.93 T in the opposite direction, how much charge flows through a point in the circuit during the change?

User Dqw
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1 Answer

4 votes

Answer:

The amount of charge that flow through a point is
\Delta q = 0.126 \ C

Step-by-step explanation:

From the question we are told that

The number of turns is
N = 100

The area is
A = 5.87 *10^(-3) m^2

The total resistance is
R = 14.9 \ \Omega

The magnetic field in first direction is
B_1 = 1.93 \ T

The magnetic field in second direction is
B_2 = -1.93 \ T

The change in magnetic field is evaluated as


\Delta B = B_1 - B_2

substituting values


\Delta B = 1.93 - [- 1.93]


\Delta B =3.2 \ T

The induced emf due to the change is mathematically evaluated as


e = NA (\Delta B )/(\Delta t )

This can also be mathematically represented as


e = IR

Where I can be mathematically represented as


I = (\Delta q )/(\Delta t)

So


e = (\Delta q)/(\Delta t ) R

Now


(\Delta q)/(\Delta t ) R = NA (\Delta B )/(\Delta t )

=>
\Delta q = (N A (\Delta B))/(R)

substituting values


\Delta q = (100 * 5.87 *10^(-3) (3.2)/(14.9)


\Delta q = 0.126 \ C

User Wasif Khan
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7.0k points