Electromagnetic Induction
State Faraday's laws of electromagnetic induction. Express Lenz's law and explain briefly how Lenz's law is in accordance with the law of conservation of energy.
A square coil of side $10\text{ cm}$ consists of 500 turns and is placed perpendicular to a uniform magnetic field of $0.4\text{ T}$. If the coil is rotated through $180^\circ$ about an axis perpendicular to the field in $0.1\text{ s}$, calculate the magnitude of the induced electromotive force (emf) in the coil.
An inductor of self-inductance $2.0\text{ H}$ carries a current of $10\text{ A}$. If the current drops uniformly to zero in $0.02\text{ s}$, calculate: (i) The average self-induced electromotive force (emf) developed across the inductor. (ii) The magnetic potential energy stored in the inductor initially.
(a) State Faraday's laws of electromagnetic induction.
(b) Derive an expression for the motional electromotive force (emf) induced across the ends of a straight conductor of length $l$ moving with a uniform velocity $v$ perpendicular to a uniform magnetic field $B$.
(c) Derive an expression for the emf induced across the ends of a metallic rod of length $l$ rotating with a constant angular velocity $\omega$ about one of its ends in a uniform magnetic field $B$ perpendicular to the plane of rotation.
(a) What is meant by Mutual Induction? Define the Coefficient of Mutual Inductance and state its S.I. unit and dimensions.
(b) Derive an expression for the mutual inductance ($M$) of two long coaxial solenoids $S_1$ and $S_2$ of equal length $l$, where solenoid $S_1$ has $N_1$ turns and radius $r_1$, and solenoid $S_2$ has $N_2$ turns and radius $r_2$ (with $r_1 < r_2$).
(c) State two factors on which the mutual inductance between two coils depends.
Derive an expression for the mutual inductance of two long coaxial solenoids of same length $L$. State the factors on which the mutual inductance of two coils depends.
A rectangular wire loop of sides $8\text{ cm}$ and $2\text{ cm}$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3\text{ T}$ directed normal to the loop. What is the electromotive force (emf) developed across the cut if the velocity of the loop is $1\text{ cm/s}$ in a direction normal to the: (a) longer side of the loop? (b) shorter side of the loop?\nFor how long does the induced voltage last in each case?
State Faraday's laws of electromagnetic induction. State Lenz's law and explain in detail how Lenz's law is a direct consequence of the law of conservation of energy.
(a) A square coil of side $10\text{ cm}$ consisting of $500$ turns is placed perpendicular to a uniform magnetic field of $0.4\text{ T}$. The magnetic field is uniformly reduced to $0.1\text{ T}$ in a time interval of $0.2\text{ s}$. If the electrical resistance of the coil is $5\ \Omega$, calculate: (i) Initial and final magnetic flux linked with the coil. (ii) Magnitude of the induced electromotive force (emf) generated in the coil. (iii) Induced current flowing through the coil. (iv) Total charge flowing through the coil during this time interval.
(b) State two methods by which the magnetic flux linked with a loop can be changed.
(a) What is meant by self-induction? Derive an expression for the self-inductance of a long air-cored solenoid. State the factors on which the self-inductance of a solenoid depends.
(b) A magnetic flux linked with a coil of $200$ turns changes from $8 \times 10^{-4} \text{ Wb}$ to $2 \times 10^{-4} \text{ Wb}$ in $0.02 \text{ seconds}$. Calculate the magnitude of induced electromotive force (emf) across the coil.