Chapter 30 - 30.1. Solve: The potential difference V...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
30.1. Solve: The potential difference Δ V between two points in space is () () f i fi x x x VVx Vx E d x Δ= = where x is the position along a line from point i to point f. When the electric field is uniform, () ( ) f i 1000 V/m 0.30 m 0.10 m 200 V x xx x VE d xE x = −Δ= =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
30.2. Visualize: Solve: The potential difference Δ V between two points on the y -axis is f i y y y VE d y Δ= When the electric field is uniform, the above result simplifies to . y y Δ =− Δ In the present problem, Δ y = y f – y i = 0.05 m – ( 0.05 m) = 0.10 m The y -component of the electric field is 50,000 V/m y E Δ V = – (–50,000 V/m)(0.10 m) = + 5.0 kV Assess: V f – V i = 5.0 kV shows that the potential at point f is higher than at point i. This is because the electric field is directed from the point at the higher potential to the point at the lower potential.
Background image of page 2
30.3. Model: The potential difference is the negative of the area under the E x vs x curve. Visualize: Please refer to Figure EX30.3. Solve: The potential difference between x = 1.0 m and x = 3.0 m is () ( ) ( ) 1 200 V/m 2.0 m 1.0 m 200 V 3.0 m 2.0 m 300 V. 2 V ⎛⎞ Δ= + = ⎜⎟ ⎝⎠ Assess: The potential difference is negative since the electric field points in the direction of decreasing potential.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
30.4. Model: The potential difference is the negative of the area under the E x vs x curve. Visualize: Please refer to Figure EX30.4. Solve: The potential difference between the origin and x = 3.0 m is () ( ) ( ) ( ) 11 3.0 m 0 m 100 V 1.0 m 0 m 200 V 3.0 m 1.0 m 22 150 V VVx Vx ⎛⎞ Δ= = = = − − + ⎜⎟ ⎝⎠ =− Thus ( ) 3.0 m 0 m 150 V 50 V 150 V 200 V VV = = Assess: The potential decreases from the origin to x = 3.0 m.
Background image of page 4
30.5. Solve: The work done is exactly equal to the increase in the potential energy of the charge. That is, () ( ) 66 fi 1.0 10 C 1.5 V 1.5 10 J WU q V q V V −− =Δ = Δ = = × = × Assess: The work done by the escalator on the charge is stored as electric potential energy of the charge.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
30.6. Solve: The Van de Graaff generator or the motor that runs the belt does work in lifting a positive ion ( q = e ) against the downward force on the positive charge that is moving up the belt. The work done is ( ) ( )( ) 61 9 6 1 3 1.0 10 V 0 V 1.60 10 C 1.0 10 V 1.6 10 J WU q V q −− =Δ = Δ = × = × × = × Assess: The work done by the generator in lifting the charge is stored as electric potential energy of the charge.
Background image of page 6
30.7. Solve: The emf is defined as the work done per unit charge by the charge escalator or the battery. That is, chem 0.60 J 12 V 0.050 C W q ε == =
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
30.8. Solve: The work done is the potential energy gained by the electron. () 19 19 2.4 10 J 1.5 V 1.6 10 C WUqV eV V = =Δ =−Δ × ⇒Δ = =− −× The potential difference from the positive to the negative terminal is –1.5 V, so the emf of the solar cell is 1.5 V.
Background image of page 8
30.9. Model: The electric field points in the direction of decreasing potential and is perpendicular to the equipotential lines.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 87

Chapter 30 - 30.1. Solve: The potential difference V...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online