Gravitational field in a region is as given as , E= 3x 2 y 2 i + 2x 3 y j. Gravitational potential at point A (1,1) is 10 unit, then what will potential at point B (2,3)

Question

Samyak Jain · Answer

We know that potentail difference between two points A and B is given by V B – V A = – ∫ E .dr with lower and upper limits as coordinates of points A and B respectively and dr = dx i + dy j + dz k . Now, E .dr = (3x 2 y 2 i + 2x 3 y j ) . (dx i + dy j + dz k ) = 3x 2 y 2 dx + 2x 3 y dy = d(x 3 y 2 ) So, V B – V A = – ∫ E .dr = – ∫d(x 3 y 2 ) = – [x 3 y 2 ] (1,1) (2,3) i.e. V B – 10 = – (2 3 .3 2 – 1 3 .1 2 ) = – 71 V B = – 71 + 10 = – 61. Potential at point B is – 61 unit.

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Gravitational field in a region is as given as , E= 3x 2 y 2 i + 2x 3 y j. Gravitational potential at point A (1,1) is 10 unit, then what will potential at point B (2,3)

Gravitational field in a region is as given as , E= 3x²y² i + 2x³y j. Gravitational potential at point A (1,1) is 10 unit, then what will potential at point B (2,3)

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Gravitational field in a region is as given as , E= 3x 2 y 2 i + 2x 3 y j. Gravitational potential at point A (1,1) is 10 unit, then what will potential at point B (2,3)

Gravitational field in a region is as given as , E= 3x2y2 i + 2x3y j. Gravitational potential at point A (1,1) is 10 unit, then what will potential at point B (2,3)

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Gravitational field in a region is as given as , E= 3x²y² i + 2x³y j. Gravitational potential at point A (1,1) is 10 unit, then what will potential at point B (2,3)