Question

Gravitational field in x-y plane is given as E = (2xhati+3Y^(2)hatj)N//kg Fin difference in gravitation potential between two points A and B, where co-ordinates of A and B are (2m, 4m) and (6m,0).

Answer 1

gravitational potential between two points A and B is 32 volts.

given, Gravitational field in X - y plane is given as

E = (2x i + 3y² j) N/kg

we know, $V=-\int\limits^b_a{E(r)}\,dr$

so, gravitational potential between two points A and B, $V=-\int\limits^B_A{E}\,dr$

= -$\int\limits^{(6,0)}_{(2,4)}{(2x\hat{i}+3y^2\hat{j}).(dx\hat{i}+dy\hat{j})}$

= -$\int\limits^6_2{2x}\,dx-\int\limits^0_4{3y^2}\,dy$

= $-[x^2]^6_2-[y^3]^0_4$

= -(6² - 2²) - (0² - 4³)

= -(36 - 4) - (- 64)

= -32 + 64

= 32 volts

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