AP Physics Multiple Choice Practice Questions on Electromagnetic Induction

“There is no democracy in physics. We can't say that some second-rate guy has as much right to an opinion as Fermi.”

–Luis Walter Alvarez

Today we shall discuss a few questions involving electromagnetic induction. Questions in this section are generally interesting and we have discussed many typical questions on various occasions on this site.

(1) A single turn plane circular conducting loop of area A and resistance R is placed in a uniform magnetic field of flux density B which has a time rate of change. The plane of the loop is perpendicular to the magnetic field. If the emf induced in the loop is V, the time rate of change of the magnetic flux density is

(a) V/A

(b) V/RA

(c) RV/A

(d) A/V

(e) AR/V

The induced emf V is  given by

             V = ∆Φ/∆t  where ∆Φ is the change of magnetic flux occurring in a small time ∆t.  

Since Φ = BA we have

             V = ∆BA/∆t  

The time rate of change of the magnetic flux density is ∆B/∆t = V/A

(2) A long straight power line carries a current I which decreases with time at a uniform rate. A plane circular conducting loop is arranged below the power line as shown in the figure. Which one among the following statements is true?

(a) No current is induced in the circular loop.

(b) A uniformly decreasing current is induced in the loop.

(c) A uniformly increasing current is induced in the loop.

(d) A steady current is induced in the loop and it flows in the anticlockwise direction

(e) A steady current is induced in the loop and it flows in the clockwise direction

Since the current in the power line is changing, the magnetic flux linked with the circular loop is changing. Therefore there must be an induced current in the loop. The induced current in the loop must be steady since the rate of decrease of magnetic flux is steady (because of the uniform decrease of current in the power line).

The magnetic field lines produced by the current in the power line are directed normally into the plane of the loop. Since the current in the power line decreases with time, the induced current in the loop must supply magnetic flux lines in the same direction, in accordance with Lenz’s law (for opposing the reduction of the flux). Therefore the induced current in the circular loop must flow in the clockwise direction [Option (e)]. 

The following questions are meant for AP Physics C aspirants:

(3) Two horizontal conducting rails AB and CD of negligible resistance are connected by a conductor BC of resistance R. Another conducting rod PQ of length L and negligible resistance can slide without friction along the rails (Fig.). The plane ABCD is horizontal and a constant magnetic field B tesla acts perpendicular to the plane ABCD. A small constant horizontal force F is applied on the slider PQ perpendicular to its length so that it slides with a constant velocity ‘v’. What is the value of the velocity v?

(a) FR/BL

(b) FR/B²L²

(c) FR/B²L

(d) FR/BL²

(e) FR²/B²L²

On applying the force F, the rod PQ starts to move from rest with an acceleration. When the rod moves the magnetic flux linked with the circuit PBCQ changes and an emf is induced in the circuit. Obviously this is the motional emf BLv.

[Note that when a conductor of length L moves with velocity ‘v’ at right angles to a magnetic field of flux density B, the motional voltage generated between its ends is BLv].

Since we have a closed circuit PBCQ, the emf BLv drives a current ‘I’ through it. PQ is therefore a current carrying conductor moving at right angles to a magnetic field. A magnetic force ILB acts opposite to the direction of motion of the conductor (in accordance with Lenz’s law). The opposing magnetic force goes on increasing with the increase in velocity of the conductor until the magnitude of the magnetic force becomes equal to that of the applied force F. The conductor thereafter continues to move with the terminal velocity acquired by it. The velocity of the rod after the initial accelerated motion is now constant.

Equating the magnitudes of the applied force F and the magnetic force ILB we have

             F = ILB

But I = BLv/R

Therefore F = B²L²v/R

This gives v = FR/B²L²

(4) An inductance L and a resistance R are connected in series with a battery and switch S as shown in the figure. The switch is closed at time t = 0. Which one among the following graphs gives the variation of the voltage V_L across the inductance as a function of time t?

There will be a voltage drop across the inductance only if the current in it changes. When the switch is closed the current in the series LR circuit will rise rapidly initially and will finally settle at the final maximum value.

[The final maximum current I₀ in the LR circuit is V₀/R where V₀ is the emf of the battery. The current I in the LR circuit during the growth at any instant t is given by

             I = I₀[1 – e^–Rt/L] where e is the base of natural logarithms]

Since the rate of variation of current is maximum initially, the voltage induced in the inductance is maximum initially. The rate of variation of current is non-linear and finally becomes zero. Therefore, the emf induced in the inductance finally becomes zero and the variation of the voltage V_L across the inductance as a function of time t is correctly represented by graph (b).

[Note that graph (d) is incorrect since the variation of the voltage is linear].

You can access all posts on electromagnetic induction on this site by clicking on the label ‘electromagnetic induction’ below this post.

 

AP Physics Kinematics Practice Questions (Multiple Choice)

“Being ignorant is not so much a shame, as being unwilling to learn.”

– Benjamin Franklin

Many questions (with solution) involving kinematics in one dimension and two dimensions have been posted on this site earlier. You may click on the label ‘kinematics’ below this post to access them. After obtaining the first result, you will have to click on the ‘older posts’ tab to access all the posts in this section. Alternatively you may try a search for ‘kinematics’ using the search box provided on this page.

Today we shall discuss a few more multiple choice practice questions on kinematics:

(1) A car travels from station A and to station B separated by a distance of d km. The average speeds of the car while covering the first and second halves of the distance are v₁ and v₂ respectively. What is the average speed of the car for the entire trip from station A to station B?

(a) √(v₁v₂)

(b) (v₁v₂)/(v₁+v₂)

(c) (v₁+v₂)/2

(d) (v₁v₂)/(v₁–v₂)

(e) (2v₁v₂)/(v₁+v₂)

The times taken for covering the first and second halves of the trip are d/2v₁ and d/2v₂ respectively.

Therefore, the total time taken to cover the entire istance d is (d/2v₁ + d/2v₂) = d[(1/2v₁) + (1/2v₂)] = d[(v₁+v₂)/2v₁v₂]

The average speed v for he entire trip is is given by

             v = d/d[(v₁+v₂)/2v₁v₂] = (2v₁v₂)/(v₁+v₂)

(2) An object has acceleration. Then

(a) its speed must be decreasing

(b) its speed must be increasing

(c) its speed must be decreasing or increasing

(d) its direction must be changing

(e) its speed or direction must be changing

An object moving with varying speed has acceleration. But this does not mean that all accelerated objects must move with a varying speed. For instance, an object in uniform circular motion has constant speed, even though it has a centripetal acceleration. Its direction of motion changes continuously and it is the change in direction that makes it an accelerated object.

For an object to be in accelerated motion, it is enough that its speed or direction of motion changes. Therefore, the correct option is (e).

(3) A bullet is fired from a gun in a direction inclined at angle θ with respect to the horizontal ground. Which one among the following graphs represents the plot of the vertical velocity v of the bullet against time t between the instant of firing and the instant just before the bullet hits the ground? (Take the upward direction as positive).

 

At the instant of firing, the bullet has the highest vertical velocity. When the bullet rises up, its vertical velocity goes on decreasing linearly (because of gravity) and at the highest point of its trajectory the vertical velocity becomes zero. The bullet then starts falling down with linearly increasing speed. In other words, the vertical velocity of the bullet becomes negative and its magnitude goes on increasing until it hits the ground.

The vertical velocity of the bullet as a function of time is therefore correctly represented by  graph (b).

(4) The adjoining figure shows forces F₁ and F₂ with their lines of action in the XY plane and acting on a particle.P.

If F₁ = a₁ î + b₁ ĵ

and F₂ = a₂ î + b₂ ĵ where î and ĵ are unit vectors in the x-direction and y-direction respectively, which one among the following statements is correct?

(a) a₁, b₁, a₂, and b₂ are positive.

(b) a₁ and  b₁ are negative where as a₂ and b₂ are positive.

(c) a₁ is negative where as b₁, a₂, and b₂ are positive.

(d) a₁, b₁ and a₂ are positive where as b₂ is positive.

(e) a₁, b₁, a₂, and b₂ are negative.

Imagine the rectangular components of F₁ and F₂. You can easily see that the x-component of F₁ is along the negative x-direction while the y-component is along the positive y-direction. The x-component of F₂ is along the positive x-direction while the y-component is along the positive y-direction.

This means that a₁ is negative where as b₁, a₂, and b₂ are positive [Option (c)].

(5) A small object at the foot of a smooth inclined plane AB (Fig.) is projected up along the inclined plane with an initial speed v. The object returns before reaching the top of the inclined plane and after reaching the foot of the plane, it moves further along a smooth horizontal surface AC. Which one among the following graphs represents the variation of the speed v of the object against time t? 

of the object therefore gets decreased uniformly and becomes zero when the object reaches its highest position on the incline. Then the object retraces its path with uniformly increasing speed until it reaches the foot of the incline. Then it moves along the horizontal surface AC with uniform speed.

The above facts are correctly represented by the  graph (d).

AP Physics B - Multiple Choice Practice Questions on Physical Optics

“One of the deep secrets of life is that all that is really worth the doing is what we do for others.”

– Lewis Carroll

Today we shall discuss a few typical multiple choice questions on physical optics:

Questions  (1) and (2) are based on the following statement:

A beam of monochromatic light having wave length λ, frequency f and intensity I in air enters a glass slab of refractive index 1.5. After traveling through the slab, the beam of light emerges through the opposite face of the slab and passes through air.

(1) Inside the slab the wave length and frequency of the light are respectively 

(a) 1.5 λ and 1.5 f

(b) λ/1.5 and f

(c) 1.5 λ and f

(d) λ and f

(e)  λ and 1.5 f

The frequency of the light is unchanged where as the speed of the light is decreased within the slab. Note that the refractive index of a medium is the ratio of the speed of light in free space (or air at ordinary pressures) to the speed in the medium. Therefore, the speed of light (v) in the glass slab is given by

            v = c/1.5 where ‘c’ is the speed of light in free space (or air).

The wave length λ, frequency f and speed v are related as

            v = f λ  

Or,       λ = v/f

Since the speed in glass is (1/1.5) times the speed in air, the wave length in glass is (1/1.5) times the wave length in air [Option (b)].

(2) The energy of the photons in glass is

(a) 1.5 times the energy in air

(b) 1/1.5 times the energy in air

(c) the same as the energy in air

(d) 3 times the energy in air

(e) 1/3 times the energy in air

The energy E of a photon is given by

             E = hf where h is Planck’s constant and f is the frequency. Since the frequency of the light is the same in both air and glass, the energy of the photons in glass is the same as the energy in air [Option (c)].

(3) White light is passing through a transparent plastic slab. Inside the slab

(a) the green component  travels with maximum speed

(b) the green component  travels with minimum speed

(c) the violet component  travels with maximum speed

(d) the red component  travels with maximum speed

(e) all components travel with the same speed

The refractive index of any transparent medium is maximum for light of violet colour and minimum for light of red colour.

[This is why violet rays are deviated most and red rays are deviated least while traveling through a glass prism, producing dispersion of white light].

The speed of light (v) in the plastic slab is given by

            v = c/n where ‘c’ is the speed of light in free space (or air) and n is the refractive inex of the slab.

Since the refractive index is the least for light of red colour, it follows that red component  travels with maximum speed [Option (d)].

(4) In an experiment with Young’s double slit, a student measures the intensity of the central maximum of the interference pattern as I. If one of the slits is covered, what will be the intensity at the position of the central maximum?

(a) I/2

(b) I/4

(c) I/(√2)

(d) I

(e) 2I

When both slits are open, suppose the resultant amplitude (of light wave) at the position of the central maximum is a. If one of the slits is covered, the amplitude at the position of the central maximum becomes a/2.

Intensity is directly proportional to the square of the amplitude. Therefore we have

            I α a² and

            I₁ α (a/2)²

 Therefore I₁ = I/4, as given in option (b).

(5) Four laser sources produce light waves y₁, y₂, y₃, and y₄ given (with usual notations) by

             y₁ = a sin ωt

             y₂ = a sin 2ωt

             y₃ = 2a sin (ωt + φ)

             y₄ = 2a sin (3ωt + φ)                                                               

Superposition of which two waves can produce interference fringes?

(a) y₁ and y₂

(b) y₂ and y₃

(c) y₃ and y₄

(d) y₁ and y₄

(e) y₁ and y₃

Waves y₁ and y₃ have the same wave length and hence they can produce interference fringes.

[The angular frequencies of y₁ and y₃ are equal].

The correct option is (e).

You will find a few useful multiple choice questions in this section here.