Fields at Work (DP IB Physics: HL)

The mass of Jupiter is m_J and the mass of its moon Europa is m_E. 

If their radii is given by r_J and r_E respectively, what is the ratio ?

A satellite of mass 2000 kg is in the Earth’s gravitational field. It moves radially from a point where the gravitational potential is –40 MJ kg^–1 to a point where the gravitational potential is –10 MJ kg^–1. What is the direction of movement of the satellite and the change in its gravitational potential energy?

Which graph shows how the kinetic energy E_K, the potential energy E_P and the total energy E of the international space station varies with distance x from the centre of Earth?

A probe is launched from the surface of the Earth, which has a radius R, at half the required escape velocity. 

What is the maximum height from the surface the probe will reach, before returning to the ground (with a bang)? 

The radius of the Sun is approximately 700 000 km. If all of its mass were compressed into a certain radius, it would collapse into a black hole, which is known to be a body from which "not even light can escape".

Which length gives the best estimate for the radius at which the Sun's mass would collapse into a black hole?

Use the following data: 

• Mass of the Sun = 2 × 10³⁰ kg
• Speed of light = 3 × 10⁸ m s^–1
• Gravitation constant = 6.67 × 10^–11 N m² kg^–2

The graph shows the variation of gravitational potential V with distance r from the centre of a spherical planet of mass M and radius R₀. 

Which statement best describes how to determine the gravitational field strength at a distance r = R from the planet?

The gravitational field strength is g and the gravitational potential is V at the surface of Earth, which has a radius of r.  

Which row in the table gives the correct value of the gravitational field strength and the gravitational potential at a height of 2r from Earth's surface? 

A particle of charge q is at point J in a uniform electric field of strength E. It is moved along a straight line joining point J to point K which is at an angle of Φ to the field lines, as shown in the diagram below. 

If the length of the path is JK, what is the change in electric potential energy of the charge q between J and K? 

Two positively charged particles, q₁ and q₂, are released from rest half-way between two oppositely charged parallel plates in a vacuum. The particles strike the negatively charged plate at the same time. 

Neglecting gravitational effects, which of the following statements is correct? 

Two charged parallel metal plates, X and Y, are separated by a distance of 2.0 m. X is charged to a potential of –180 V and Y is charged to a potential of +180 V. 

What is the magnitude and direction of the electric field strength at a point exactly mid-way between plates X and Y? 

A proton with velocity of 1.5 × 10⁷ m s⁻¹ moves normally into a uniform magnetic field of flux density 0.30 T. Which is the best estimate of the radius of curvature of the path of the proton?

The diagram shows a uniform electric field in which equipotential lines are placed 3.0 cm apart.

A charge of –6.0 nC is placed at the equipotential line X.

Which of the following statements is correct?

The diagram shows four point charges at the corners of a square of sides 4a.

What is the electric potential at P, the centre of the square?

The Earth has radius, r and mass M. Which expression could be used to calculate the minimum time, T of one Earth-day for the material at the equator to just remain on the surface?

A space probe with mass m is launched from the surface of the Earth’s equator into orbit. The total energy E_t given to the space probe is:

where G is the gravitational constant and M and r_E are the mass and radius of Earth.

What is the height of the space probe’s orbit above the Earth’s surface?

Two satellites, X and Y, of equal mass, orbit a planet at radii R and 2R respectively.

Which one of the following statements is correct?

A cable used in high-voltage electrical transmission has a radius of 3.0 mm. The diagram shows the circular cross-section of the cable with electrical field lines denoting areas of equipotential.

In the instant shown the potential of the cable is + 600 000 V.

Assuming that the diagram has been drawn to scale, what is the the potential gradient near the surface of the cable?

Two identical negative point charges, P and Q, are separated by a distance of 6.0 mm. The resultant electric potential at point M, which is mid–way between the charges, is –40 V.

What would be the resultant electrical potential at a point 2.0 mm closer to Q?

Observations are made on two separate planetary system's suns of mass M₁ and mass M₂.

Their orbiting planets, P₁ and P₂ have masses of m₁ and m₂, and are observed to have identical orbits in shape and magnitude. P₁ completes an orbit in a quarter of the time taken by P₂.

Which statement can astronomers reasonably deduce?

Two points charges of +4Q and –Q are placed 150 mm apart.

Which of the following graphs shows the variation of the potential V against the distance x along the line joining the two point charges?