(a) Define self-inductance of a coil. Obtain an expression for the ene

1.	(a) Define self-inductance of a coil. Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current though it grows from zero to ‘I’. (b) A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm s−1 till it goes out of the field. (i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist? (ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time. OR (a) Draw the magnetic field lines due to a circular loop area →A carrying current I. Show that it acts as a bar magnet of magnetic moment →m=I→A (b) Derive the expression for the magnetic field due to a solenoid of length ‘2l’, radius‘a’having ’n’ number of turns per unit length and carrying a steady current ‘I’ at a point on the axial line, distance ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?
Answer» (a) Define self-inductance of a coil. Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current though it grows from zero to ‘I’. (b) A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm $s^{- 1}$ till it goes out of the field. (i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist? (ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time. OR (a) Draw the magnetic field lines due to a circular loop area $\to A$ carrying current I. Show that it acts as a bar magnet of magnetic moment $\to m = I \to A$ (b) Derive the expression for the magnetic field due to a solenoid of length ‘2l’, radius‘a’having ’n’ number of turns per unit length and carrying a steady current ‘I’ at a point on the axial line, distance ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?

(a) Define self-inductance of a coil. Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current though it grows from zero to ‘I’. (b) A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm s−1 till it goes out of the field. (i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist? (ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time. OR (a) Draw the magnetic field lines due to a circular loop area →A carrying current I. Show that it acts as a bar magnet of magnetic moment →m=I→A (b) Derive the expression for the magnetic field due to a solenoid of length ‘2l’, radius‘a’having ’n’ number of turns per unit length and carrying a steady current ‘I’ at a point on the axial line, distance ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?

Answer»

(a) Define self-inductance of a coil. Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current though it grows from zero to ‘I’.

(b) A square loop MNOP of side 20 cm is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of 20 cm $s^{- 1}$ till it goes out of the field.

(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?

(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.

(a) Draw the magnetic field lines due to a circular loop area $\to A$ carrying current I. Show that it acts as a bar magnet of magnetic moment $\to m = I \to A$

(b) Derive the expression for the magnetic field due to a solenoid of length ‘2l’, radius‘a’having ’n’ number of turns per unit length and carrying a steady current ‘I’ at a point on the axial line, distance ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?

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