Question

An electric field of \( 20 N C ^{-1} \) exists along the \( x \)-axis in space. Calculate the potential difference \( V_{B}-V_{A} \) where the points \( A \) and \( B \) are given by, (a) \( A=(0,0) ; B=(4 m , 2 m ) \) (b) \( A=(4 m , 2 m ) ; B=(6 m , 5 m ) \) (c) \( A=(0,0) ; B=(6 m , 5 m ) \). Do you find any relation between the answers of parts (a), (b) and (c)?

Answer 1

(a) A = (0, 0), B = (4, 2)

The displacement in the X-direction is 4 m.

The potential difference in the space due to electric field is:

V_B − V_A = E × d

= 20 × 4

= 80 V

(b) A = (4m, 2m), B = (6m, 5m)

The displacement between the two points will be 2 m in X-direction.

Therefore, the potential difference is given as:

⇒ V_B − V_A = E × d

= 20 × 2

= 40 V

(c) A = (0, 0), B = (6m, 5m)

The displacement in the X-direction is 6 m.

The potential difference in the space due to electric field is:

V_B − V_A = E × d

= 20 × 6

= 120V