Amperes law provides another method to determine the magnetic field due to a given current distribution.

Line integral of the given magnetic field  around any closed curve is equal to  times the net

Magnetic field due to an infinite sheet carrying current: The figure shows an infinite sheet of current with linear current density j (A/m). Due to symmetry the field line pattern above and below the sheet is uniform. Consider a square loop of side l as shown in the figure.

According to Ampere's law,       .

Since B ^ dl along the path b → c and d → a, therefore,  ;

Also, B || dl along the path a → b and c → d, thus 

The current enclosed by the loop is i = jl

Therefore, according to Ampere's law  or B = μ_oj/2

Solenoid: A cylindrical coil of many tightly wound turns of insulated wire with generally diameter of the coil smaller than its length are called a solenoid.

One end of the solenoid behaves like the North Pole and opposite end behaves like the South Pole. As the size of the solenoid increases, the interior space converts into more uniform and the external field becomes weaker.

A magnetic field is produced around and within the solenoid. The magnetic space within the solenoid is parallel and uniform to the axis of solenoid.

            Magnetic field under the solenoid at position P is given by 

(ii) Infinite length solenoid: If the solenoid is of infinite length and the point is well inside the solenoid.

            So B_in = μ_oni  

(iii) If the solenoid is of infinite length and the point is near one end i.e. a=0 and b = π/2 

            So B_end = 1/2(μ_oni)                        

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