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Electric Shielding: A Conundrum
A thin layer of conducting material, such as a sheet of copper, is placed between a point charge and a free charge. What effect will the shielding have on the free charge if it is (i) positive and (ii) negative, respectively?
Magnetic Field of a Solenoid
A long solenoid with 200 turns per meter and a current of 5 A is placed near a compass. The compass needle shows deflection. Assuming the Earth's magnetic field is negligible, determine the direction of the magnetic field at the compass and the number of turns per meter required to produce a magnetic field of 0.5 T at the compass, given the current is doubled to 10 A.
Magnetic Field Around a Coil?
A current-carrying coil of 50 turns is placed in a horizontal plane. The current flowing through the coil is 2A. At a distance of 10cm from the coil's center, a magnetic field of 5 x 10^-6 T is measured using a magnetometer. How will the magnetic field strength change if the number of turns in the coil is doubled, while keeping the current and distance constant?
Electric Field due to Spherical Shell?
A spherical shell of radius 10 cm has a total charge of 4 μC uniformly distributed over its surface. If a tiny test charge of -2 μC is placed at the centre of the shell, will it experience any net electric field and what would be its direction?
Cascading Capacitors: A Charging Conundrum?
Three capacitors of capacitances 2 μF, 3 μF, and 4 μF are connected in cascade. If a potential difference of 12 V is applied across the combination, determine the potential difference across each capacitor and the total charge stored in the circuit. Assume the capacitors are initially uncharged and the charging process is ideal.
Induction in a Coil?
A coil of insulated copper wire is connected to an ammeter and a galvanometer in series. When a magnet is brought near the coil, the galvanometer shows a deflection, but the ammeter does not. Explain the reason behind this observation, and suggest a method to improve the sensitivity of the galvanometer reading.
Capacitance in Parallel: A Surprising Twist?
When two capacitors of different capacitances are connected in parallel, does the total capacitance always increase? Consider a circuit where one capacitor has a capacitance of 10 μF and the other has a capacitance of 20 μF. What happens to the total capacitance when they are connected in parallel?
Two Insulators in Contact?
When a glass rod and an ebonite rod are brought into contact and separated again, an ebonite rod is found to be negatively charged. Explain the process that occurs during contact and the resulting charge distribution on the two rods.
How does a capacitor protect electronic devices from power surges?
A small electronic device is connected to a power source through a capacitor. A sudden increase in voltage causes the power source to surge. How can the capacitor effectively reduce the impact of this surge on the device?
Induction Loop vs. Coils?
Consider a situation where you need to detect metal objects in a security scanner. You have two options: use a single loop of wire or use multiple coils of wire. Compare and contrast the two approaches, highlighting the advantages and limitations of each in terms of sensitivity, speed, and cost. Which one would you prefer, and why?
Magnetic Field of a Current-Carrying Loop?
A circular loop of insulated copper wire, carrying a constant current of 5 A, is placed in a uniform magnetic field. How would the magnetic field inside the loop change if the current in the loop is reversed?
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?
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