Question

Conservative Forces It takes work to lift an object under the influence of the Earth's gravitational force. This increases the gravitational potential energy of the object. Lowering the ob- ject releases the gravitational potential energy that was stored when it was lifted. When you studied the gravitational force, you applied the term conservative to it because it allows the recovery of all of the stored energy. You have now found experimentally that the work required to move an object under the influence of the gravitational force is path independent. This is an important property of any conservative force. Given the mathematical similarity between the Coulomb force and gravita- tional force laws, it should come as no surprise that experiments confirm that the Coulomb force is also conservative. Again, this means that the work needed to move a charge is independent of the path taken between the points. And from the definition of work is the work done by the electric field E to move a small test charge q between points A and B.
Sorry this problem has so many parts--thank you in advance for your effort.

Answer 1

Part (1-7)

Given:

Distance moved by charge is AB = d unit. ( Along Electric field)

Test charge is +q

Direction of Electric field is from A to B

From the defination of work =w

^w= $\dpi{150} \bg_white \sum_{A}^{B}$ ^{qEcos$\dpi{150} \bg_white \theta$$\dpi{150} \bg_white \Delta$S ( where $\dpi{150} \bg_white \theta$ = angle between elcetric field}    vector and displacement vector)

$\dpi{150} \bg_white \Delta$S is displacement from A to B

W = q * E * cos 0° * d

( $\dpi{150} \bg_white \theta$ = 0° as displacement vector is along E vector)

and d = $\dpi{150} \bg_white \Delta$

w = (q* E * d ) J

Part (1-8)

Part (1-9)

part (1-10)