A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is −3 Q , and it is insulated from its surroundings ( Fig. P22.44 ). (a) Derive expressions for the electric-field magnitude E in terms of the distance r from the center for the regions r < a , a < r < b , and r > b . What is the surface charge density (b) on the inner surface of the conducting shell; (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the | location of all charges, (e) Graph E as a function of r . Figure P22.44
A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is −3 Q , and it is insulated from its surroundings ( Fig. P22.44 ). (a) Derive expressions for the electric-field magnitude E in terms of the distance r from the center for the regions r < a , a < r < b , and r > b . What is the surface charge density (b) on the inner surface of the conducting shell; (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the | location of all charges, (e) Graph E as a function of r . Figure P22.44
A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is −3Q, and it is insulated from its surroundings (Fig. P22.44). (a) Derive expressions for the electric-field magnitude E in terms of the distance r from the center for the regions r < a, a < r < b, and r > b. What is the surface charge density (b) on the inner surface of the conducting shell; (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the | location of all charges, (e) Graph E as a function of r.
Figure 8.14 shows a cube at rest and a small object heading toward it. (a) Describe the directions (angle 1) at which the small object can emerge after colliding elastically with the cube. How does 1 depend on b, the so-called impact parameter? Ignore any effects that might be due to rotation after the collision, and assume that the cube is much more massive than the small object. (b) Answer the same questions if the small object instead collides with a massive sphere.
2. A projectile is shot from a launcher at an angle 0,, with an initial velocity
magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a
child's noggin (see Figure 1). The apple is a height y above the tabletop, and a
horizontal distance x from the launcher. Set this up as a formal problem, and solve
for x. That is, determine an expression for x in terms of only v₁, 0, y and g.
Actually, this is quite a long expression. So, if you want, you can determine an
expression for x in terms of v., 0., and time t, and determine another expression for
timet (in terms of v., 0.,y and g) that you will solve and then substitute the value of
t into the expression for x. Your final equation(s) will be called Equation 3 (and
Equation 4).
Draw a phase portrait for an oscillating, damped spring.
Chapter 22 Solutions
University Physics, Volume 2 - Technology Update Custom Edition for Texas A&M - College Station, 2/e
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