A conductor ball of radius R is charged with charge Q0. The ball is placed in an infinite space filled with a material with conductivity σ and permittivity ε, so the charge leaks away from the ball.
Find the remaining charge on the ball as function of time!
Click here to read the solution.
Showing posts with label electromagnetics. Show all posts
Showing posts with label electromagnetics. Show all posts
A semicircle arc is charged with charge density distribution at a point, , where λ is total charge in a unit length and α is angle between the diameter and its position.
Calculate the ratio of electrical potential at point A and point O!
Click here to read the solution.
Consider 2 capacitors with same areas in series as shown in the picture. One of them is placed between the another one's plates. The wider capacitor have capacitance C and have distance twice of the narrower one.
Calculate the net capacitance of the circuit!
Click here to read the solution.
Consider a spherical-shells capacitor made by two spherical shells that have different radius. The smaller spherical shell is placed inside the larger one without touching each other.
Initially, the two spherical shells are concentric, and then the smaller shell is moved slightly, so they're no longer concentric.
How's the change of its capacitance? Increase, decrease, or remain same?
Two parallel-plate capacitors, A and B, have same area, but separation of plates in capacitor B is a half of A's. The capacitors are in parallel and connected to a voltage source with emf V. Then you insert capacitor B into capacitor A, like shown below.
Calculate the work done by you!
Assume capacitance of capacitor A is C and B is 2C. Ignore edge effect of capacitors.
(If you want a more challenging problem, assume the capacitor is in series, not in parallel)
Consider a thin cylinder's shell with radius r and mass m (inertia mr^2). Two sides of the surface have different characteristics. Outer surface of the shell is a conductor with resistivity ρ and thickness δ (δ<<r). And the inner surface is an insulator which is charged uniformly with surface charge density σ.
A torque τ works on the cylinder. Find the angular acceleration α of the cylinder when its angular velocity is ω!
Assume that magnetic field inside the cylinder is uniform and equals to magnetic field at the middle.
A long solenoid with self-inductance L and radius r is connected to an AC voltage source with frequency ω and max voltage V. Then a thin cylindrical shell with the same length and the same cross-section area with the solenoid is inserted into middle of the solenoid without touching it. It has thickness δ (δ<<r) and resistivity ρ.
Ignore resistance of the solenoid. No current between the solenoid and the cylinder.
Proof that this system is equal to a system where the solenoid is in series with a resistor! Determine the resistance R of this resistor! Assume the system is in vacuum.
Also assume that magnetic field inside the solenoid and the cylinder is uniform and equals to magnetic field at the middle.
A capacitor consists of two parallel identical plates with area A and mass m. The plates are movable and initially separated by a distance d (d^2 is much smaller than A). Between the plates, there is an insulator spring connecting the two plates. Its spring constant is k and its relaxed length is d. The system is placed in vacuum.
The capacitor is then connected to a voltage source with emf V. As it's connected, the two plates start oscillating.
Determine the condition so that the plates can do oscillation!
(Only consider one dimensional movement and ignore energy loss)
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