Under the influence of the Coulomb field of charge , a charge is moving around it in an elliptical orbit. Find out the correct statement(s). [2009]

Question

Under the influence of the Coulomb field of charge $+ Q$ , a charge $- q$ is moving around it in an elliptical orbit. Find out the correct statement(s). [2009]

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(1)

According to the question, under the influence of the Coulomb field of charge $+ Q$ , a charge $- q$ is moving around it in an elliptical orbit. This situation is shown in the figure which is similar to a planet revolving around the Sun.

The distance of $- q$ from $+ Q$ is changing; therefore, the force between the charges will change. The speed of the charge $- q$ will be greater when the charge is nearer to $+ Q$ as compared to when it is far. Hence, the angular velocity of charge $- q$ is not constant.

The direction of the velocity changes continuously; therefore, the linear momentum is not constant. The angular momentum of charge $(- q)$ about $Q$ is constant because the torque about charge $+ Q$ is zero.

Solution

Q.
Under the influence of the Coulomb field of charge $+ Q$ , a charge $- q$ is moving around it in an elliptical orbit. Find out the correct statement(s). [2009]

1 The angular momentum of the charge $- q$ is constant

2 The linear momentum of the charge $- q$ is constant

3 The angular velocity of the charge $- q$ is constant

4 The linear speed of the charge $- q$ is constant

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Solution

Q. Under the influence of the Coulomb field of charge +Q, a charge −q is moving around it in an elliptical orbit. Find out the correct statement(s). [2009]

1 The angular momentum of the charge −q is constant

2 The linear momentum of the charge −q is constant

3 The angular velocity of the charge −q is constant