Question

In: Physics

A regular icosahedron, as shown in the figure, has an outer radius (defined as the distance...

A regular icosahedron, as shown in the figure, has an outer radius (defined as the distance from the centre to a vertex) of 9.51 cm and an inner radius (defined as the distance from the centre to the centre of a face) of 7.56 cm. It has 20 faces which are equilateral triangles with side length 10.0 cm, and 12 vertices.
Twelve negative charges of magnitude 20.0 μC are placed at the vertices and 20 positive charges of magnitude 12.0 μC are placed at the face centres. A positive charge of Q = +44.25 μC is placed at the centre of the icosahedron.

  1. What is the force acting on the charge at the centre of the icosahedron? [1]

  2. If one of the negative charges at a vertex is removed, what is the force on the charge at the centre of the icosahedron? [2]

  3. If one of the positive charges at the face is removed, what is the force on the charge at the centre of the icosahedron? [2]

  4. Using your answers to parts ii) and iii) what is the net force on the charge Q at the centre if a complete face (i.e. one positive charge and the three surrounding negative charges), is removed? [5]

Solutions

Expert Solution

genius_generous answered 2 years ago
Next > < Previous

Related Solutions

A toroidal solenoid (see the figure ) has inner radius 14.1cmand outer radius 18.6 cm...
A toroidal solenoid (see the figure ) has inner radius 14.1cm and outer radius 18.6 cm . The solenoid has 270 turns and carries a current of 7.30 A. Part A What is the magnitude of the magnetic field at 11.8 cm from the center of the torus? Part B What is the magnitude of the magnetic field at 16.3 cm from the center of the torus? Part C What is the magnitude of the magnetic field at 20.4 cm from the center of the torus?
Consider the 12 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with an inner radius of 0.255 m and an outer radius of 0.32 m.
Consider the 12 kg motorcycle wheel shown in the figure. Assume it to be approximately a ring with an inner radius of 0.255 m and an outer radius of 0.32 m. The motorcycle is on its center stand, so that the wheel can spin freely.         33% Part (a) If the drive chain exerts a force of 2250 N at a radius of 4.8 cm, what is the angular acceleration of the wheel, in radians per square second?...
The radius of the roll of paper shown in the figure is 7.6 cm and its...
The radius of the roll of paper shown in the figure is 7.6 cm and its moment of inertia is I = 2.9 × 10-3 kg·m2. A force of 2.9 N is exerted on the end of the roll for 1.1 s, but the paper does not tear so it begins to unroll. A constant friction torque of 0.11 m·N is exerted on the roll which gradually brings it to a stop. Assume that the paper's thickness is negligible. (a)...
The Roche Radius, defined to the orbital distance at which a satellite tidally torn apart by...
The Roche Radius, defined to the orbital distance at which a satellite tidally torn apart by the parent body, is named after Edward Roche, who first derived it in 1848. Recall that his radius is given by: d = r*( 2 * M/m )^(1/3)   Where r is the radius of the satellite, m is the mass of the satellite, and M is the mass of the parent body. (a) Recast this equation in terms of the density of the satellite...
The Roche Radius, defined to the orbital distance at which a satellite tidally torn apart by...
The Roche Radius, defined to the orbital distance at which a satellite tidally torn apart by the parent body, is named after Edward Roche, who first derived it in 1848. Recall that his radius is given by: )1/3 d=r (2 M m Where r is the radius of the satellite, m the mass of the satellite, and M is the mass of the parent body. (a) Recast this equation in terms of the density of the satellite (m), the density...
A long straight cylindrical shell has an inner radius Ri and an outer radius R0.
A long straight cylindrical shell has an inner radius Ri and an outer radius R0. It carries a current I, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r < Ri). The magnetic field is zero everywhere outside the shell (r > R0).We conclude that the wire: A) is on the cylinder axis and carries current I in the same direction as the current in the shell B) may be anywhere in...
A spherical shell has in inner radius Ri and an outer radius Ro. Within the shell,...
A spherical shell has in inner radius Ri and an outer radius Ro. Within the shell, a total charge Q is uniformly distributed. Calculate: a) the charge density within the shell (if you cannot get this answer, you can proceed without it). b) the electric field strength E(r) outside the shell (r > Ro). c) the electric field strength inside the shell (r< Ri). d) the electric field within the shell (Ri < r < Ro) e) show that your...
A coaxial cylindrical conductor with outer radius R2 and inner radius R1 and has dielectric Er...
A coaxial cylindrical conductor with outer radius R2 and inner radius R1 and has dielectric Er relative dielectric between the conductor. Is the charge per unit length on the Anner cylinder is lemda, find (a) D, E for a <r<b ( (b) potential difference between the conductors (c) the capacitance per unit length.
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It...
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length ?? where ? is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +?. Part E Calculate the magnitude the electric field in terms of ? and the distance r from the axis of the tube for r>b. Express your answer...
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It...
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +?, where ? is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +?. Part A Calculate the electric field in terms of ? and the distance r from the axis of the tube for r<a. Part B Calculate the electric...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT