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How does a capacitor store electric charge?
A 2 μF capacitor is connected to a 12 V battery. Calculate the electric charge stored on the plates of the capacitor when the switch is closed. Assume the capacitor behaves as an ideal capacitor. Also, explain why the capacitor does not allow the current to flow when the switch is closed.
Induction's Time-Domain Response?
Consider a long solenoid carrying a current of 2 A. Suddenly, the current is switched off. Describe and explain the nature of the induced electromotive force (e.m.f.) in the solenoid as a function of time, assuming the magnetic flux through the solenoid is 0.02 Wb.
Capacitance of a Parallel-Plate Capacitor?
A parallel-plate capacitor is made of two plates, each 5 cm x 10 cm in size, separated by a 2 mm thick dielectric material. The plates are 1 cm apart when empty. How will the capacitance change if the gap between the plates is reduced to 1 mm and the dielectric material is replaced with a different one of double the dielectric constant?
Magnetic Field of a Current Carrying Wire?
A long, straight wire carries a current of 20 A in a direction perpendicular to the plane of the paper. Two identical loops, each having a radius of 0.1 m, are placed symmetrically on either side of the wire. One loop is made of copper (conductivity = 5.8 × 10^7 S/m) and the other of a non-ferromagnetic material (conductivity = 3.0 × 10^7 S/m).
Capacitance in a Real-World Scenario?
A parallel plate capacitor is used in a fire alarm system. The plates are 5 cm apart and have an area of 0.05 m^2. The dielectric constant of the material between the plates is 3. The capacitance of the capacitor is 2 μF. How would you modify the capacitor to increase its capacitance by 50%?
Potential Differences in a Circuit?
Suppose you are designing a portable power bank with a capacity of 20,000 mAh. The power bank uses a rechargeable battery with an internal resistance of 0.5 Ω and an external resistance of 10 Ω in series. How would you determine the maximum potential difference across the power bank's terminals during charging, and what factors would you consider to minimize this potential difference?
Induction in a Coiled Wire?
A coiled wire is placed in a magnetic field. When the magnetic field is reduced by a factor of two in a time period of 1 second, and the radius of the coil is increased by 20%, what happens to the induced emf? Explain your reasoning with calculations to justify the effect on the emf.
Lifting a Magnet: What Happens?
Imagine you're holding a magnet suspended above a copper wire coil in a circuit. When you suddenly lift the magnet, the coil begins to generate a current. Explain why this happens and discuss the direction of the induced current in the coil.
Minimum Power Transfer Theorem?
In an AC circuit containing a resistor and an inductor, a variable capacitor is connected in parallel with the inductor. The capacitor's capacitance is slowly reduced from a very large value to a very small value. What happens to the power consumed by the inductor in the circuit as the capacitance reduces?
Capacitor in Parallel: Equivalent Capacitance?
A circuit consists of two 4 μF and 6 μF capacitors connected in parallel. If a 12 V battery is connected across the circuit, calculate the equivalent capacitance and the charge stored in each capacitor.
Motion of a Charged Particle in a Magnetic Field?
A charged particle with mass 9 × 10^-31 kg and charge 1.6 × 10^-19 C is moving at a speed of 5 × 10^6 m/s perpendicular to a magnetic field of strength 0.5 T. How will the particle's trajectory change if the magnetic field is doubled to 1 T? Explain your reasoning in terms of the force on the particle due to the magnetic field.
Capacitor Connection Conundrum?
A 40 μF capacitor and a 20 μF capacitor are connected in series across a 400 V power supply. If the two capacitors are then disconnected from the power supply and connected in parallel, how much charge will be stored in each capacitor in the parallel configuration?
Conservation of Energy in a Circuit?
In an LCR series circuit with an AC voltage source, a resistor, an inductor and a capacitor are connected in series. When the circuit is connected to a power source, a current flows through the circuit. On the other hand, when the circuit is disconnected from the power source, the same components are left isolated and free to oscillate. How is energy conserved in this circuit during these two different scenarios?
Parallel Plate Capacitor's Real-World Application?
A parallel plate capacitor is used to regulate the voltage in a high-voltage television display system. The capacitor acts as a filter, ensuring that the voltage remains within a specified range. If the capacitance of the capacitor is doubled, what change would you expect in the TV display system's performance?
Magnetic Materials: Pros and Cons?
You are the director of a company that produces magnetic materials. Design and discuss a magnetic material that you would recommend for use in a hospital, explaining its advantages and disadvantages in terms of safety, durability, and cost-effectiveness.
Charges Inside a Conducting Sphere?
A conducting sphere of radius 2m has a charge of 4 mC uniformly distributed over its surface. You are asked to place a charge of +2 mC at its center. Describe the distribution of charges on the surface of the sphere after the charge is placed inside.
Induction in Non-Conductors?
A researcher has shown that electromagnetic induction can occur in a non-conducting dielectric material. However, this effect is only significant when the material undergoes mechanical stress or changes in temperature. Does this observation contradict the basic principle of electromagnetic induction?
Effect of Shielding on Electric Field?
Consider a point charge of +3 μC placed at a distance of 2 meters from a large conducting spherical shell of radius 1 meter. If a small hole is made in the shell at the point closest to the charge, how does the electric field strength at the surface of the shell change compared to when the shell is intact?
A Capacitor in Music?
The Forensic Electronic Music System uses a variable capacitor to control the pitch of a synthesizer. If the capacitor has a maximum capacitance of 1000 pF and is connected to a 9 V battery, calculate the maximum allowable change in distance between the plates to ensure that the pitch changes smoothly over a musical range of 3 octaves?
Magnetic Field of a Current-Carrying Loop?
A circular loop of wire with a radius of 10 cm carries a current of 5 A. If the loop is placed in a uniform magnetic field of 0.5 T, what is the direction and magnitude of the magnetic field produced by the current-carrying loop at its center?
Magnetic Field due to Current: Conceptual Dilemma?
A long, straight wire carries a current of 10 A from east to west, and a circular wire of radius 5 cm carries the same current in the same direction. Determine the magnetic field at a point on the axis of the circular wire, 5 cm away from its center, and compare it with the magnetic field at the same point due to the long wire.
How does a solenoid's magnetic field influence its surrounding environment?
Consider a long solenoid carrying a current. You are the chief engineer designing a nearby laboratory. Describe the region around the solenoid where you would not allow students to stand, explaining the phenomenon that makes this area hazardous for them.
Magnetic Domains: A Study of Hysteresis?
A ferromagnetic material is heated above its Curie temperature and then cooled slowly to form a hysteresis loop. Explain the reasons behind the asymmetry of the hysteresis loop and its relation to the magnetic domains within the material.
Motion of Charged Particles in Electric Fields?
A particle of mass 5 × 10^(-4) kg and charge 3 × 10^(-8) C is placed in an electric field of strength 5 × 10^4 N/C. The particle starts moving in the field. Explain, with the help of a suitable diagram, how the direction of the force on the particle changes when the direction of the electric field is reversed, keeping the field strength the same.
Magnetic Field Around a Wire?
A wire carrying a current of 2 A is bent into a circular shape with a radius of 0.2 m. If the magnetic field at the centre of the circle is measured to be 4 × 10-7 T, what is the direction and magnitude of the magnetic field at a point on the circumference of the circle, 0.1 m away from the centre?
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