A point charge $$2 \times 10^{-2}$$ C is moved from $$P$$ to $$S$$ in a uniform electric field of $$30$$ N C$$^{-1}$$ directed along positive $$x$$-axis. If coordinates of $$P$$ and $$S$$ are $$(1, 2, 0)$$ m and $$(0, 0, 0)$$ m respectively, the work done by electric field will be

Solution :

Work done by electric field is given by :

$$W = q\vec{E}\cdot\vec{d}$$

Given :

$$q = 2 \times 10^{-2}\text{ C}$$

Electric field is along positive x-axis :

$$\vec{E} = 30\hat{i}\ \text{N C}^{-1}$$

Coordinates :

$$P(1,2,0)$$

$$S(0,0,0)$$

Displacement from P to S :

$$\vec{d} = (0-1)\hat{i} + (0-2)\hat{j}$$

$$= -\hat{i} -2\hat{j}$$

Now,

$$\vec{E}\cdot\vec{d} = 30\hat{i}\cdot(-\hat{i}-2\hat{j})$$

$$= -30$$

Therefore,

$$W = (2 \times 10^{-2})(-30)$$

$$= -0.6\text{ J}$$

Final Answer :

$$-0.6\text{ J}$$