Questions from Electronics

Q: A rocket ship leaves earth at a speed of /

A rocket ship leaves earth at a speed of / When a clock on the rocket says 1 hour has elapsed, the rocket ship sends a light signal back to earth. (a) According to earth clocks, when was the signa...

Q: A Lincoln Continental is twice as long as a VW Beetle,

A Lincoln Continental is twice as long as a VW Beetle, when they are at rest. As the Continental overtakes the VW, going through a speed trap, a (stationary) policeman observes that they both have the...

Q: Check the divergence theorem for the function v = r 2

Check the divergence theorem for the function v = r 2 sin θ rˆ + 4r 2 cos θ θˆ + r 2 tan θ φˆ, using the...

Q: Prove that [A × (B × C)]+ [

Prove that [A × (B × C)]+ [B × (C × A)]+ [C × (A × B)]= 0. Under what conditions does A × (B × C) = (A × B) × C?

Q: Here are two cute checks of the fundamental theorems: (

Here are two cute checks of the fundamental theorems: (a) Combine Corollary 2 to the gradient theorem with Stokes’ theorem (v=∇T, in this case). Show that the result is consistent with what you alread...

Q: Although the gradient, divergence, and curl theorems are the fundamental

Although the gradient, divergence, and curl theorems are the fundamental integral theorems of vector calculus, it is possible to derive a number of corollaries from them. Show that: (a) / where c is a...

Q: The integral / is sometimes called the vector area

The integral / is sometimes called the vector area of the surface S. If S happens to be flat, then |a| is the ordinary (scalar) area, obviously. (a) Find the vector area of a hemispher...

Q: (a) Find the divergence of the function /

(a) Find the divergence of the function First compute it directly, as in Eq. 1.84. Test your result using the divergence theorem, as in Eq. 1.85. Is there a delta function at the origin, as there was...

Q: In case you’re not persuaded that ∇2(1/r

In case you’re not persuaded that ∇2(1/r) = −4πδ3(r) (Eq. 1.102 with rr = 0 for simplicity), try replacing r by and watch...

Q: (a) Twelve equal charges, q, are situated at

(a) Twelve equal charges, q, are situated at the corners of a regular 12-sided polygon (for instance, one on each numeral of a clock face). What is the net force on a test charge Q at the center? (b)...