A copper wire has a square cross section 2.1 mm on a side. The wire is 4.3 m long and carries a current of 3.6 A. The density of
free electrons is 8.5 * 1028>m3 . Find the magnitudes of (a) the current density in the wire and (b) the electric field in the wire. (c) How much time is required for an electron to travel the length of the wire?
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The magnetic field vector B generated by the current at an arbitrary point in terms of i, the length element dl, and the vector for the distance r from dl to the point is given by the equation dB = μ0/4 π ∫ (dl x r)/r
The Biot – Savart Law gets its name from Jean-Baptiste Biot and Felix Savart. This is a formula that describes the relationship between force, displacement, and velocity. It plays a huge role in the branch of electromagnetism. This law is used to derive the equation between the magnetic field which is produced due to the flow of a constant electric current.
The equation of Biot – Savart law is
dB = μ0/4 π ∫ {(idl sinΦ)/r2}
Here,
I is the current,
dl is the small length of the wire. As the direction of this length is along the current hence it forms the vector idl.
r is the position vector of the point in question which is drawn from the current element and
Φ is the angle between the two.
<h3>Applications of Biot – Savart Law </h3>• It helps in the calculation of magnetic field in an infinitely long straight wire with constant current,
• Calculation of magnetic field in the center of current carrying arc can be done by this,
• To calculate the magnetic field along the axis of a circular current carrying coil, this law can be used.
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To develop this problem it is necessary to apply the concepts related to the Dopler effect.
The equation is defined by
Where
= Approaching velocities
= Receding velocities
c = Speed of sound
v = Emitter speed
And
Therefore using the values given we can find the velocity through,
Assuming the ratio above, we can use any f_h and f_i with the ratio 2.4 to 1
Therefore the cars goes to 145.3m/s