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​:
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

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​:

Induced emf is proportional with rate of change in magnetic flux. As the distance between the bar magnet and loop magnetic flux changes and the rate of change increases as the relative velocity increases (vL>vK=vM​).

Therefore, εL>εK=εM​

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.

Explanation​:

Because the electric field lines point toward the charge $q$, this charge must be negative, meaning that statement I is false.

The relatively greater number of field lines around charge $q$ means that this charge magnitude is greater than the charge +Q, indicating that statement II is also untrue.

Electric field line density is proportional to electric field strength. Because the field line density near $q$ is greater than that near $+Q$, statement III is correct.

Therefore the correct answer is option C.

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)

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 pattern of equipotential surfaces belongs to two like charges. That indicates that field direction at points A and B should be in the same direction. Additionally, field lines and equipotential surfaces are at right angles to each other. The only answer that satisfies these conditions is A. Therefore, the answer is A.

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​:
Summing the four electric field vectors from the individual point charges, the fields from the charge at the top left and the bottom right will cancel out. The fields from the bottom left and top right will add together to give a net field in the direction of the charge in the top right.

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.

Explanation​:
The $20nC$ charge produces a leftward electric field in region 1. Therefore, the electric field generated by the $X$ charge should be rightward to cancel the electric field of the 20 nC charge. This is achieved by a negative charge at X. The magnitude of the electric field decreases by distance. All locations in region 1 are closer to point charge $X$ than they are to the $20nC$ charge. Therefore X should be smaller than the charge of $20nC$. The answer is D.

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​:
Centripetal acceleration of an orbiting satellite is the gravitational acceleration of the planet, which is given by

g=GM/r^2

Since the gravitational acceleration is inversely proportional to the square of the orbital radius, the correct graphical representation is given in C

1/4

Explanation​:

Statement I is incorrect. This is due to Newton’s Law of Gravitation. The astronaut will experience gravitational force from the Earth that acts as the centripetal force.

Since the centripetal force is the gravitational force, then the centripetal acceleration is equal to the gravitational field strength at that point. Therefore both the astronaut and the space station experience the same acceleration. Then statements II and III are correct.