Ampere's Law Problem Solving Tips

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  • Ampere's law in magnetism is similar to the Gauss's law in electrostatics.
  • With the help of this law we can find the magnetic fiels caused by symmetric current configurations.
  • Statement:-"The line integral B.dl around any closed path equals μ0I ,where I is the net steady curent passing through any surface bounded by a closed path. Mathematically
    B.dl = μ0I
    where integral is evaluated along a closed path.
  • Without going into the details of how to prove the law I will give you some handy things to remember while solving problems using Ampere's law.
    1. If B is everywhere tangent to the path of integration and has same magnitude B at every point on the amperian loop then the line integral becomes equal to B times the circumfrance of the path.
    2. If B is everywhere perpandicular to the amperian loop or over some portion of the loop then that portion of the loop does not make any contribution to the line integral because B.dl = Bdlcos90 = 0
    3. In the integral ∫B.dl B is the the total magnetic field at each point in the path i.e., field at any point P on the loop is due to both current sources inside and outside the Amperian loop . However the integral ∫B.dl is always zero for currents outside the Amperian loop.
    4. Things should be keept in mind before choosing the Amperian loop that points at which field is to be determined must always lie on the Amperian loop and the path or the loop must have enough symmetry so that line integral can easily be evaluated.

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