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?

The amount of charge that flow through a point is

Explanation:

From the question we are told that

    The number of turns is  

    The area is  

       The total resistance is

       The magnetic field in first direction  is  

        The magnetic field in second   direction  is

The change in magnetic field is evaluated as

substituting values

The induced emf due to the change is mathematically evaluated as

This can also be mathematically represented as

     Where I can be mathematically represented as

So  

Now  

=>  

substituting values

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west