OpenStax University Physics/Archived sample/T1V2

PhysicsCalc2152657831440

PhysicsCalc2:T1:V2
PhysicsCalc2152657831440 1) A proton is accelerated (at rest) from a plate held at 333.6 volts to a plate at zero volts. What is the final speed?
 * a) 1.1 x 105 m/s.
 * b) 1.7 x 105 m/s.
 * c) 2.5 x 105 m/s.
 * d) 3.8 x 105 m/s.
 * e) 5.7 x 105 m/s.

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at  (x,y) =( 5a, 4a) is &beta;kQ/a2, where &beta; equals
 * a) 1.76 x 10-3 unit
 * b) 2.13 x 10-3 unit
 * c) 2.59 x 10-3 unit
 * d) 3.13 x 10-3 unit
 * e) 3.79 x 10-3 unit

3) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?
 * a) 0.91 J.
 * b) 1.05 J.
 * c) 1.21 J.
 * d) 1.39 J.
 * e) 1.6 J.

4) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 5
 * b) 1&minus;s
 * c) 5&minus;s
 * d) s&minus;1
 * e) s&minus;4

5) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (1.86+2.43z)\rho^2\hat\rho +9.75z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.
 * a) 6.201E+02
 * b) 7.513E+02
 * c) 9.102E+02
 * d) 1.103E+03
 * e) 1.336E+03

6) How fast is a 2355 eV electron moving?
 * a) 1.9 x 107 m/s.
 * b) 2.9 x 107 m/s.
 * c) 4.3 x 107 m/s.
 * d) 6.5 x 107 m/s.
 * e) 9.7 x 107 m/s.

7) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
 * a) 1826 N.
 * b) 2099 N.
 * c) 2414 N.
 * d) 2776 N.
 * e) 3193 N.

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at  (x,y) =( 1.1a, 1.2a) is &beta;kQ/a2, where &beta; equals
 * a) 2.86 x 10-1
 * b) 3.47 x 10-1
 * c) 4.2 x 10-1
 * d) 5.09 x 10-1
 * e) 6.17 x 10-1

9) A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s&minus;7
 * b) 8
 * c) s&minus;3
 * d) 7&minus;s
 * e) 3&minus;s

10) Integrate the line integral of $$\vec F = 2xy\hat x + 9.7x\hat y $$  from the origin to the point at x = 2.8 and y = 3.2
 * a) 5.26E+01
 * b) 5.62E+01
 * c) 6.02E+01
 * d) 6.44E+01
 * e) 6.89E+01

11) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * a) 2
 * b) 1/2
 * c) 3
 * d) 2/3
 * e) 3/2

12) A cylinder of radius, r=3, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as, $$\vec\mathfrak F = (2.37+2.6z)\rho^2\hat\rho +8.84z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{side}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the curved side surface of the cylinder.
 * a) 7.465E+02
 * b) 9.044E+02
 * c) 1.096E+03
 * d) 1.327E+03
 * e) 1.608E+03