A positive point charge +Q is fixed in space. A negative point charge -q of mass m revovles around fixed charge in elliptical orbit. The fixed charge +Q is at one focus of the ellipse, $\vec{r}$ is the position vector of negative charge from positive point charge and v its velocity when it is at general point P. The only force acting on negative charqe is the electrostatic force due to positive charge. Then which of the following statements is/are true.
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$| \vec{r} \times \vec{V} |$ remains constant as negative point charge moves from A to B

Total energy of system is conserved

$| \vec{r} \cdot \vec{v} |$ first increases and then decreases as negative charge moves from A to B

$| m \vec{v} |$ of the negative point charge is constant

answer is B, C, D.

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Detailed Solution

Since net force on negative charge is always directed towards fixed positive charge, the torque on negative charge about positive charge is zero. Therefore angular momentum of negative charge about fixed positive charge is conserved.

$T h e a n g l e b e t w e e n \vec{r} a n d \vec{v} f i r s t d e c r e a s e s f r o m 90^{0} t o a m i n i m u m t h e n a g a i n i n c r e a s e s t o 90^{0} . a s - q m o v e s f r o m A t o B . A s a r e s u l t \vec{r} . \vec{v} f i r s t i n c r e a s e s f r o m z e r o t o m a x i m u m, t h e n a g a i n d e c r e a s e s t o z e r o .$