More Examples of Magnetic Flux Biot-Savart Law Ampère’s Law

Question 1: A current in a conductor produces B, which can be calculated using the Biot-Savart law. Since current is defined as the rate of flow of charge, what can we conclude about the magnetic field caused by stationary charge?

Example 1: A cube of length L=2.5 cm is positioned as shown below. There is a uniform magnetic field throughout the region given by the expression B=(5i+4j+3k) T. a) calculate the flux through the shaded face of the cube b) what is the total flux through the six faces of the cube? L B

Solution

Example 2: A closed current path shaped as shown below produces a magnetic field at P. If the arc subtends an angle of 30 0 and the total length of the wire is 1.2m, what are the magnitude and direction of the field produced at P if the current in the loop is 3.0 A ? P 30 0

Solution

Example 3: For the arrangement shown in the figure below, the current in the long, straight wire has value I 1 =5 A and lies in the plane of the rectangular loop, which carries a current I 2 =10 A. The dimensions are a=0.15m, c=0.1m and L=0.45m. Find the net force exerted on the rectangle by the magnetic field of the straight current-carrying conductor. I1I1 I2I2 c a L

Solution

Example 4: A long cylindrical conductor of radius R carries a current I. The current density J, however, is not uniform over the conductor but is a function of radius according to J=br, where b is a constant. Find an expression for the magnetic field B at: a) r R

Solution