1. A point charge is moved between two parallel plates separated by a distance of $5cm$. The potential difference between the points is $50V$.

What is the average electric field E?

2. Two positive charges of magnitude $2C$ and $8C$ respectively are placed 9cm apart. A third charge is introduced between the two charges as shown below;

At what separation, X, from the 2C charge is the electric field strength equal to zero?

3. A charged particle is moving horizontally when it enters an electric field between two parallel plates. The path followed by the particle when it passes through the plates is shown. Assume gravitational effects to be negligible.

Which statements are correct about the charged particle?

• I. The particle is positively charged.
• II. A magnetic field in a direction into the page could cause the charged particles to move horizontally without deflection.
• III. A magnetic field in a direction out of the page could cause the charged particles to move horizontally without deflection.

4. A satellite of mass $m$ is in an orbit at a height $h$ from the surface of a planet of mass $M$. The centripetal force acting on the satellite is $F$ and the linear speed is $v$.

What is the new centripetal force and linear orbital speed when it is moved to a new orbit at $2h$ from the surface of the planet?

5. A charge of $X$ and a charge of $20nC$ are held at a fixed distance.

A point where the electric field is zero can only be found in region 1. Which of the following statements is true about the charge on $X$?

6. An astronaut in a space station orbiting the earth experiences weightlessness.

The following are three statements about the astronaut and the space station:

• I.  The astronaut experiences no gravitational force.
• II.  The centripetal acceleration of the space station is equivalent to the gravitational field strength at that location
• III.  Both the astronaut and the space station have the same acceleration.

Which of these statements is correct?

7. A proton and another object with charge +e exert electrical and gravitational forces on one another. To the nearest order of magnitude, what mass must the object have to be so that the net force acting on it is zero?

8. Two charges, separated by a large distance, are shown below, along with the electric field lines around each charge.

Which of the following statements is correct?

• I.  The charge $q$ is positive.
• II.  The charge $q$ is equal in magnitude to $+Q$.
• III.  The electric field magnitude near the charge $q$ is greater than the magnitude of the field near the charge $+Q$.

9. The gravitational field strength on the surface of the moon is gE/6. Two objects of different masses $m$ and $2m$ are released with zero speed on the moon from heights of $h$ and $2h$, respectively, where $h$ is small compared to the radius of the moon.

What are the magnitudes of the accelerations of these objects right after release?

10. Two positive charges q1 and q2 are separated by a distance $d$. A third positive charge $q$ is placed at a distance d/4 from q1 so that the charge $q$ is in equilibrium.

What is the ratio q1/q2?

11. Two point charges are separated by a distance $r$ as shown.

12. Four fixed charged point particles are at the vertices of a rectangle. Which arrow represents the net electric field at the center of the rectangle?

13. Planet $A$ has a gravitational field strength $g$ at its surface. Planet $B$ has twice the density and twice the radius of planet $A$.

What is the gravitational field strength at the surface of $B$?

14. The diagram below shows a circuit connected to an iron rod $XY$. The connecting wires are flexible. The rod is placed in a magnetic field directed perpendicularly into the page as shown.

In what direction will the resultant force act on the rod when the current is switched on in the circuit?

15. A plastic rod carrying a uniformly distributed positive charge is bent into a quarter-circle. What is the direction of the electric field at point $P$?

16. In the following diagram, the size of the charges is small compared to the distance R.

What is the direction of the force on the charge in the center?

17. Two objects A and B are separated by a distance $r$. The mass of A is much larger than that of B.

Which of the following is correct about magnitude and direction of the gravitational force exerted by A on B compared to that exerted by B on A?

18. Satellites $A$ and $B$ orbit the same planet of mass $M$. Satellite $A$ has a mass of $3m$ and it is located at a height of $R$ from the surface of the planet. Satellite $B$ has a mass of $m$ and it is located at a height of 2$R$ from the surface of the planet.

What is the ratio of the centripetal force acting on $A$ to the centripetal force acting on $B$?

19. The centers of three masses lie on the same line. The centers of the masses are separated as shown.

The net gravitational force on m2 is zero when the value of $d$ is one third of $x$. What is the ratio m1/m3?

20. Satellite $A$ of mass $M$ orbits a planet with an orbital speed $v$ and orbital radius $R$. Another satellite $B$ with mass $3M$ orbits the same planet with the same orbital speed.

21. Which of the following is correct about the gravitational field strength at a point near a planet?

22. A beam of electrons enters a uniform electric field, as shown.

What effect does this field have on the horizontal and vertical components of the electrons' velocity?

23. A satellite is in a circular orbit of radius $R$ around a planet of mass $M$. Which of the following graphs represents the relationship between the centripetal acceleration of the satellite and its orbital radius?

A.				B.
C.				D.

24. Estimate the speed of an alpha particle that has accelerated from rest in a uniform electric field E=50NC^−1 over a distance of 2.0m.

25. Which of the following graphs shows the variation of the gravitational field strength of a planet with distance $r$ from the surface of a planet?

A.			B.
C.			D.