5.154 Charge of elementary particles

Problem 5.154:What is the charge of $(i)$ electron $(ii)$ proton and $(iii)$ neutron? Solution: Charge of $(i)$ electron$ = - \:1.6 \times 10^{-19}\:C$                            $(ii)$ Proton$ = + \:1.6 \times 10^{-19}\:C$                            $(iii)$ Neutron=...

5.153 Power dissipation in RC circuit

Problem 1.153: Determine the rate of energy dissipation in the given circuit at steady state. Solution: Current flows in a capacitor only when it is charging or discharging. At steady state situations current through capacitor is zero. So the given circuit can be...

5.152 Energy stored in capacitor

Problem 1.152: Determine the energy stored in the capacitor in the given circuit at steady state. Solution: Current flows in a capacitor only when it is charging or discharging. At steady state situations current through capacitor is zero. So the given circuit can be...

5.151 Charge in a capacitor

Problem 1.151: Determine the charge in the capacitor in the given circuit at steady state. Solution: Current flows in a capacitor only when it is charging or discharging. At steady state situations current through capacitor is zero. So the given circuit can be redrawn...

5.150 Current in RC circuit

Problem 1.150: Determine the current flowing from the cell in the given circuit at steady state. Solution: Current flows in a capacitor only when it is charging or discharging. At steady state situations current through capacitor is zero. So the given circuit can be...

5.147 Induced e.m.f in a straight rod

Problem 5.147: A composite conductor is moving with a  speed of V as shown in the diagram. The magnetic field is inward to the plane and has a constant strength of B everywhere. Find the potential difference induced in the rod.  Solution: When a straight conductor of...

5.145 Frequency of current in ac generator

Problem 5.145: The armature of an ac generator is rotated with a speed of 3000 rotations per minute. What will be the frequency of current produced in it? Solution: When a coil with $N$ number of turns each of area $A$ is rotated in a magnetic field $B$ with an...

5.144 Mutual induction between a pair of circular coils

Problem 5.144: A circular coil of radius $r$ is kept at the center of another circular coil of very large radius $R$ as shown. Determine the mutual induction between the coils. Solution: If a current $i$ is established in one coil, the current produces a magnetic flux...

5.143 Magnetic flux linkage between two circular coils

Problem 5.143: A circular coil of radius $r$ is kept at the center of another circular coil of very large radius $R$ as shown. Current $I$ flows in the larger coil. What is the magnetic flux linked with the inner coil? Solution: The current in the larger coil will...

5.142 Time period of a bar magnet in a magnetic field

Problem 5.142: A magnetic needle has magnetic moment $6.7\times 10^2\: Am^2$ and moment of inertia $7.5\times 10^6\: kg m^2$. It performs $10$ complete oscillations in $6.70\: s$. What is the magnitude of the magnetic field? Solution: Time period is the time taken for...

5.141 Potential energy of a dipole in a magnetic field

Problem 5.141: Four identical magnets are placed in a uniform magnetic field as shown. Which magnet possesses the minimum potential energy?   Solution: If a magnet of magnetic moment $\vec{M}$ is placed in a uniform magnetic field of intensity $\vec{B}$, then the...

5.139 Magnetic field due to current carrying conductor

Problem 5.139: A straight wire carries a steady current of $10\:A$ and is placed along the y axis of a the coordinate system. Determine the magnitude and direction of the magnetic field at a point $(4\:m, 0)$. Solution: Magnetic field due to a very long thin wire...

5.138 Magnetic moment of a solenoid

Problem 5.138: A closely wound solenoid of 2000 turns and area of cross-section $1.6\times 10^{-4}\: m^2$, carrying a current of $4.0 \:A$, is suspended through its center allowing it to turn in a horizontal plane. What is the magnetic moment associated with the...

5.137 Magnetic moment of a needle

Problem 5.137: A thin needle of magnetic moment $M$ is bend into a semicircle. What is the new magnetic moment? Solution: Magnetic moment of a magnet is defined as the product of pole strength and shortest distance between its poles. Let the length of the magnetic...

5.136 Coercivity of a subbstance

Problem 5.136: A current of $1A$ flowing in the 1000 turns of a solenoid of length $10\:cm$ can completely demagnetize a  soft iron bar of length $4\:cm$ and area of cross section of $2\:cm^2$. Determine the coercivity of the material. Solution: Coercivity is the...