According to ampere’s circuital law line integral of the magnetic field is equal to u0 times of the net current or the sum of total current passing through the which is closer from its ends means closed loop.
Standard Definition Of One Ampere –
It two infinitely long wires are placed at the distance of one meter from each other and the current flowing through the both of the infinitely long wires is equal then if the force per unit length acting between the two infinitely long wires is 2 x 10 -17 N/m then the value of current passing through the infinitely long wires will be one ampere.
Applications Of The Ampere Circuital Law –
- To find out the magnetic field due to a current-carrying long infinite wire with the help of ampere circuital law- Consider a long infinite current-carrying wire in which current ‘I’ is flowing and we want to find the magnetic field at distance d from the infinitely long wire which is perpendicular to the infinitely long wire. Consider a circular loop of radius considering the point P at which the magnetic field is to be found. we consider an element DL on the circular loop where the magnetic field and DL are in the same direction.
- To find the magnetic field due to a current-carrying cylindrical conductor with the help of ampere circuital law (for hollow cylindrical conductor)- Consider a hollow cylindrical conductor of radius r and we want to find out the magnetic field due to this conductor at a point P at a distance r.
- To find out the magnetic field due to a current-carrying cylindrical conductor with the help of ampere circuital law( For solid cylindrical conductor)- Consider a solid cylinder conductor of radius ‘r’ are and we want to find out the magnetic field due to this conductor at a point P at a distance r.
Note- If the current is flowing in the same direction in both the infinitely long wires then the magnetic force will be of the attractive nature and if the direction of current is opposite in the infinitely long wires then the magnetic force will be e of the repulsive nature.
Magnetic force and magnetic torque acting on a current-carrying rectangular loop- Consider a rectangular loop of length l and having its width which is b then the current flowing in the rectangular loop will be I. This rectangular loop is placed in a strong magnetic field b then the magnetic force will act on each side of the rectangular loop. The magnetic field applied or acting on the rectangular loop is denoted by F1 and F2.
Show F1 and F2 are acting on the loop which are in opposite directions but the magnitude of the magnetic force is the same. Both of the magnetic forces will act as a couple on the body and will tend to move the body in rotatory motion. Net magnetic force on the loop will be equal to zero because the magnetic forces are in opposite directions and each of the magnetic forces will cancel out each other.
Torque acting on a rectangular loop-
When a rectangular loop is placed in a uniform magnetic field then the rectangular loop will experience magnetic force on the two opposite sides which are equal in case of magnitude while it is opposite in case of the direction. These magnetic forces will rotate the rectangular loop.
According to this law, the current which is flowing in a conducting wire starts flow from south direction to the north direction then the magnetic needle which is placed over the wire will reflect towards the west direction.
Expression For Fringe Width In Young’s Double-Slit Experiment –
In Young’s double-slit experiment, there are two narrow slits which are S1 and S2 and these small slits are separated from each other by the distance of d. A screen is placed at a distance D from the slits and the center point of the screen is o. A point P is at distance y from o at which bright fringe or the dark Fringes are found. Slits are illuminated by monochromatic light source then fringe width can be calculated.