Question

The electric field in a region is given by

`vecE = (10x + 4)hati`

where x is in m and E is in N/C. Calculate the amount of work done in taking a unit charge from

1. (5 m, 0) to (10 m, 0)
2. (5 m, 0) to (5 m, 10 m)

Answer 1

`vecE = (10x + 4)hati`

We have W = Vq

⇒ `V = W/q = W/1 = W`

Now, applying V = −∫Edx

i. `W = V = -int_6^10(10x + 4)dx`

= `-[5x^2 + 4x]_5^10`

= −[5 × (100 − 25) + 4(10 − 5)]

= −(5 × 75 + 4 × 5)

= −395 J

ii. Moving the unit positive charge from (5m, 0) to (5m, 10) requires no work due to its perpendicular displacement from the field.