Explanation​:
The force acting on the electron is downward at entry and perpendicular to the velocity, and the electron has negative charge. Using conventional methods (right-hand/left-hand) the magnetic field vector points into the plane of the paper

Explanation​:
Recall that magnetic force acts perpendicular to current flow according to the Fleming Left hand rule. That immediately eliminates option A and D. Then using the right hand grip rule, we can determine that the magnetic field experienced by wire $Y$ points into the page. The force direction and magnetic field direction allows current direction to be found with Fleming’s left-hand rule.

Explanation​:
According to Newton's third law, the two objects exert equal and opposite forces on each other.

The equation

• Fg=GMm/r​

also shows that the forces on the planets are equal in magnitude.

Explanation​:
The electric field vector inside a hollow conductor is zero. Due to the lack of field inside the sphere, the electric potential is constant and equal to the surface value . Outward from the surface of the sphere, the electric field varies with the inverse​ square of the distance from the center while electric potential decreases inversely with the distance from the center.

Explanation​:
Choice A is incorrect as it equates the gravitational field strength with the gravitational force and these two are two different physical quantities.

Choice B is the correct answer, since the gravitational field strength equals to force per unit mass; g=F/m​.

Choice C is incorrect, because the gravitational field strength is inversely proportional to the square of the distance between the center of mass of the planet and that point; g=GM/r^2​.

Choice D is incorrect, because the gravitational field strength depends on the mass of the planet; g=GM/r^2​.

Explanation​:
Conventional current will flow anticlockwise due to the orientation of the cell. To determine the force experienced by a current carrying conductor in a magnetic field, use (any appropriate hand-rule convention or) Flemming's left hand rule which states that if we arrange our thumb, forefinger and middle finger of the left-hand perpendicular to each other, then the thumb points towards the direction of the force experienced by the conductor, the forefinger points towards the direction of the magnetic field and the middle finger points towards the direction of the electric current.

According to Fleming’s left hand rule, the electrons in the rod experience a force towards Side B at the top of the rod. The flow of electrons (negative charges) towards the top end of the rod will stop when the electrons at that end are numerous enough to push new electrons back by electrostatic repulsion. That is, an electric field is established in the rod where the top is negative and the bottom is positive. The corresponding field is from the bottom to the top (Side D to Side B)

Explanation​:
The direction of the current is perpendicular to the magnetic field in both regions and the magnitude of the field is unchanged. So the magnitude of the force is $F$.

Using Fleming's left hand rule, direction of the force is

Explanation​:
I is correct as the gravitational force is given by F=GMm/r^2​

II is incorrect because gravitational field strength is the gravitational acceleration, which is not equivalent to the force.

III is correct because the gravitational force is the only force acting on the satellite and it provides the centripetal force

Explanation​:

When the bar magnet moves towards and away from the ring, the magnetic flux through the ring will change. According to Lenz's law, an emf, and therefore a current is induced to oppose the change in the flux. So as the bar magnet approaches the metal ring, the metal ring moves to the right due to repulsive forces that resist the decrease in distance between the ring and the magnet. Likewise, as the bar magnet moves away from the metal ring, the metal ring moves to the left.

Explanation​:
The electric field strength direction is the same as the direction of the electric force.

The electric field will be directed out of the rod in all directions, as it contains uniformly distributed positive charges.

Getting the vector sum for the electric field, due to symmetry the total electric field strength will be directed out of the rod with an angle away from the midpoint of the rod as shown

Also we can think of B as the only correct solution, because it’s a positively charged rod, so the direction must be out of the rod.

Explanation​:

The hydrogen nucleus is a proton, so it has positive charge.

The electric field lines are pointed upwards, meaning the higher potential is below the nucleus, or meaning that the force on the nucleus is upward.

The question asks for the largest work done, therefore we are looking for the largest displacement parallel and in the opposite direction the field lines. This is shown in D.

Explanation​:
The gravitational field strength varies inversely with the square of the distance from the center of the planet ($R$) to a given point.

g=GM(R)^2​

This means the variation of the gravitational field strength with $R$ is an inverse square law. Note, however, that the question asks for the relationship from the distance from the surface of the planet, therefore the graph starts at a finite value of field strength at the surface ($r=0$), then follows the shape of an inverse square curve.

4g

Explanation​:
I: A can only be kinetic energy as kinetic energy is always positive

II: B is the total energy as it has the same magnitude as the kinetic energy but is negative, and the sum of the value of graph A and graph B at all times

III: C is the gravitational potential energy as given in the data booklet (Ep=−GMm/r), therefore the statement is wrong

Explanation​:
A is incorrect because the equipotentials have equal potential difference but the lines are not equally spaced.

B is incorrect because work =qΔV=(−e)[−30 V−(−50 V)]=−20 eV

C is correct because work =qΔV=(−e)[−30 V−(−10 V)]=20 eV

D is incorrect because work done from R to S is zero (same potential)

Explanation​:
The negative ion is attracted by the positive charge, therefore its energy at the inner equipotential line is less than the outer one.

Moving from 1 to 2, it moves to a lower energy, therefore work is negative

Moving from 2 to 3, it moves along the same equipotential line, therefore no work done

Moving from 3 to 4, it moves to a higher energy, therefore positive work is done.

Explanation​:
At a level closer to the surface of the planet, the centripetal force increases. In a circular orbit, the centripetal force is provided by the gravitational force, which is proportional to the inverse square of the distance from the center of the planet.

The kinetic energy in a closer orbit is larger since the centripetal force is larger. Making the speed larger is necessary to maintain the orbit, which therefore increases the kinetic energy.

Explanation​:
Because the electric field is only in the vertical direction, it does not affect the electrons' horizontal speed.

As described by E=F/q in the data booklet, the electrons do experience a vertical force which causes them to accelerate vertically.

Therefore when they enter the electric field, the horizontal speed of the electrons remains the same while their vertical speed increases