1. 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.

2. 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 $P$?

3. Two stars of equal mass $M$ are shown in the diagram, distance $d$ apart. A planet is equidistant from the two stars, with distance d/2​ across the midpoint of the line joining the stars as shown.

What is the resultant gravitational field strength at the position of the planet due to the two stars?

4. 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 $B$?

5. A source of radiation is near a magnetic field that is directed into the page. A sheet of paper is placed in the path of the radiation before it enters the magnetic field.

The gamma radiation is not deflected when entering the magnetic field. Which of the following is correct about the other type of radiation that penetrates the paper sheet and the direction of its deflected path in the magnetic field?

6. A current-carrying wire is at right angles to a uniform magnetic field. The magnetic force per unit length on the wire is F/L. The length of the wire, the magnitude of the magnetic field strength, and the current of the wire are all doubled. Which of the following is the magnetic force per unit length on the wire after these changes?

7. 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?

8. 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?

9. An object of mass $m$ and charge $q$ is dropped vertically between two parallel plates, $K$ and $L$. A magnetic field $B$ can be created perpendicular to the plane of the paper. The electric field between plates is $E$.

Which of the following is correct about the magnitude of magnetic and electric fields when the object falls vertically at a constant velocity v?

10. 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?

11. 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 $B$?

12. A wire is carrying a current $I$ is placed in a region of uniform magnetic field B1​. The magnitude of the magnetic field is $B$, and its direction is into the page. The force acting on the wire is $F$, as shown in the diagram.

The wire, carrying the same current $I$, is now placed with the orientation shown into another region of uniform magnetic field B2​. The magnitude of the magnetic field is $B$, and its direction is out of the page.

What is the correct direction and magnitude of the force acting on the wire in field B2​?

	Direction	Magnitude
A.		$F$
B.		$F$
C.		$F\sin \theta$
D.		$F\sin \theta$

13. An electron enters a region of magnetic field with a velocity as shown in the diagram. The path followed by the electron is shown by the dotted line. What is the direction of the magnetic field in this region?

14. 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​​?

15. The diagram shows the gravitational field between two masses m1 and m2​.

Which of the following is correct?

16. A positive and a negative charge of equal magnitude are located on the same horizontal line.

What is the direction of the net electric field at the point marked X, equidistant from the two charges?

17. 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 $+Q$.

18. Which of the following correctly lists the fundamental forces in decreasing order of strength?

19. 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.

20. 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​​?

21. 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?

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

23. Planet $X$ has radius $R$ and density $\rho$. The gravitational field strength at the surface of Planet $X$ is $g$.

What is the ratio of the gravitational field strength at the surface of planet Y, which has radius 0.25$R$ and density 3$\rho$, to that at the surface of Planet X?

24. 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?

25. Two charges separated by a distance $r$ are placed in a medium with permittivity $ϵ$. The charges are then moved to air so that they have the same force between them as that in the medium.