(a) To prove: That the vertical component of force on a point P due to a small polar rectangle of size Δ r × Δ θ located at distance r .

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Answer 1

Question

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

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(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}. Calculate the integral f(x, y, z) dv. E

(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

Answer 2

Question

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

Expert Solution & Answer

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Answer 4

Question

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

Expert Solution & Answer

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Answer 5

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

Answer 6

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

Answer 7

Chapter 16.5, Problem 58E

To determine

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

Answer 8

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

Answer 9

To determine

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

(a) To prove: That the vertical component of force on a point P due to a small polar rectangle of size Δ r × Δ θ located at distance r .

Solution Summary: The author explains how the vertical component of force exerted on a point P by the polar rectangular disk is F = k Q

Videos

(a)

To prove:

That the vertical component of force on a point P due to a small polar rectangle of size $Δ r \times Δ θ$ located at distance r.

(b) A

To compute:

The force by evaluating the integral set up in previous part.

$F = k Q ρ \int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{a}^{b} \frac{\cos (θ)}{r^{2}} r d r d θ$

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Chapter 16 Solutions

(a) To prove: That the vertical component of force on a point P due to a small polar rectangle of size Δ r × Δ θ located at distance r .

Solution Summary: The author explains how the vertical component of force exerted on a point P by the polar rectangular disk is F = k Q

Videos