Explanation:

Using the right-hand rule, one can determine the direction of magnetic fields on loops $Y$ and $Z$ due to the current in the wire.

The magnetic field on loop $Y$ is in the direction out of the page, and the magnetic field on loop $Z$ is in the direction into the page. Both decrease as the current in the wire decreases, so magnetic flux decreases for both loops $Y$ and $Z$.

According to Lenz' law, a current is induced on the loop $Y$ in an anti-clockwise direction, so it opposes the change in the flux. Likewise, according to Lenz' law, a current is induced on the loop Z in a clockwise direction, so it opposes the change in the flux.

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:

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:

• I. Correct: Since the particle is deflected toward to negative plate it is positively charged.
• II. Correct: In order not to be deflected magnetic force acts on the particle should be upwards. According to the right hand rule the magnetic field should be into the page.
• III. Incorrect: In order not to be deflected magnetic force acts on the particle should be in upwards. According to the right hand rule magnetic field should be into the page.

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

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 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:
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:
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:
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:
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:
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.

• ε=BvL
• power = ε^2/R=[(BvL)^2]/R=B^2v^2L^2/R

Explanation:
The alpha particle has positive charge, therefore its deflection will be in the opposite direction of the electron. (answer A or B)

It has a larger mass, therefore the acceleration will be much smaller, explained by the following calculation:

• qE=ma
• a=qE/m

The alpha particle has twice the charge of the electron, this doubles its acceleration.

It has much more mass than the electron, therefore the denominator in the above ratio increases by a larger factor than the numerator. This means the acceleration of the alpha particle will be much smaller than that of the electron. (its motion will change at a slower rate).

This can also be explained by 2-dimensional motion where there is no force on the horizontal but there is a smaller force on the vertical, meaning it will cover the vertical distance in a longer time, allowing it to travel further along the horizontal, giving the path in B.

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.

The electric field at X due to -Q points toward -Q. The field at X due to +Q points away from +Q, with the same magnitude at X as the field from -Q. Adding the electric field vectors gives a vector pointing to the left.

Explanation:
Equipotential lines are perpendicular to field lines, which means the field lines must be directed from A to B or vice versa. That is only possible for 2 charges with opposite sign. In I and II, the forces from the two objects would be in opposite directions, giving a resultant field zero at the midpoint, and equipotential lines of a “peanut” shape.

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:

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.