The system consists of four thin concentric spherical

Question

1. The system consists of four thin concentric spherical shells with radii R, 2R, 3R, and 4R, respectively. The surface charge densities on these shells are 4σ, -3σ, 2σ, and - σ, respectively. Determine the electric field in all regions.

2. Two capacitors (disconnected from the power sources) with capacitances C₁ and C₂ contain charges 1 and q₂, respectively. What happens to the energy of these capacitors when they are connected in parallel? Discuss possible sources or drains of the excess energy. Find the conditions when the energy remains the same.

3. Earth's magnetic field represents the field of a magnetic dipole. If one assumes that this field is created by the circle current in the equatorial plane at the distance 5000 km from the Earth center, what is the magnitude of this current? The Earth radius is 6350 km and the magnetic field near the magnetic pole is 0.0001 T.

4. A point charge q is held a distance a above an infinite grounded conducting plane. When released, the charge starts to move toward the plane. Neglecting gravitation, determine the charge velocity when it hits the plane. (Hint: Use the energy conservation law.) Discuss the physical sense of obtained result.

Answer 1

Be sure to properly read all the questions of resistance and capacitors illustrated below and provide solution by applying the appropriate concepts and laws. Q1. The system comprises 4 thin concentric spherical shells having radii R, 2R, 3R and 4R correspondingly. The surface charge densities on such shells are 4s, -3s, 2s and - s. Find the electric field in all areas. Q2. Two capacitors (detached from power sources) having capacitances C1 and C2 have charges 1 and q2. What happens to energy of such capacitors if they are joined in parallel? Describe possible sources or drains of the surplus energy. Determine the conditions if the energy remains similar. Q3. The magnetic field of earth symbolizes the field of magnetic dipole. If one supposes that this field is made by the circle present in the equatorial plane at distance 5000 km from the Earth center, determine the magnitude of this current? The Earth radius is 6350 km and the magnetic field close to magnetic pole is 0.0001 T.