If i, j, k represent unit vectors (vectors whose magnitude of 1) along the x, y,

Question

If i, j, k represent unit vectors (vectors whose magnitude of 1) along the x, y, and z axis respectively, assume E field is in the +i direction and a test charge +qo is moving along the +i from point A to point B then is VB-VA is < or > or = 0. [Draw a line and show the location of A and B and then write the answer giving a proper explaination]

The first case is:

1) E along i, test charge +qo moving along +i

potential decreases from A to B

____A_____B_____VB<VA so VA-VB>0

Repeat for the 7 other cases such as if q0 is a -charge or E is a -field etc. or E is along +i but +q0 moving along -i (similar to other situations). In each case find VB-VA clearly showing the location of A and B with proper explaination.

-I have read through some similar chegg Q and A for this problem but I am still having difficulty.

Explanation / Answer

electric field travels from high potential to low potential hence

Vb < Va

so Vb - Va < 0

case 2 :

E = towards negative X-direction

electric field travels from high potential to low potential hence

Vb > Va

so Vb - Va > 0

Case 3 :

E = towards Positive X-axis

q = negative charge

electric field travels from high potential to low potential hence

Vb < Va

so Vb - Va < 0

Case 4:

E = towards negative X-direction

electric field travels from high potential to low potential hence

Vb > Va

so Vb - Va > 0

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