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A UHF television loop antenna has a diameter of 11 cm. The magnetic field of a TV signal is normal to the plane of the loop and, at one instant of time, its magnitude is changing at the rate 0.16 T/s. The magnetic field is uniform. What emf is induced in the antenna

Answers

Answer 1

Answer:

-0.00152 V

Explanation:

Parameters given:

Diameter of the loop = 11 cm = 0.11m

Rate of change of magnetic field, dB/dt = 0.16 T/s

Radius of the loop = 0.055m

The area of the loop will be:

A = pi * r²

A = 3.142 * 0.055²

A = 0.0095 m²

The EMF induced in a loop of wire due to the presence of a changing magnetic field, dB, in a time interval, dt, is given as:

EMF = - N * A * dB/dt

In this case, there's only one loop, so N = 1.

Therefore:

EMF = -1 * 0.0095 * 0.16

EMF = -0.00152 V

The negative sign indicates that the current flowing through the loop acts opposite to the change in the magnetic field.

Answer 2

Answer:

Answer:

The induced emf is 0.00152 V

Explanation:

Given data:

d = 11 cm = 0.11 m

$r=(d)/(2) =(0.11)/(2) =0.055m$

The area is:

$A=\pi r^(2) =\pi *(0.055^(2) )=0.0095m^(2)$

The induced emf is:

$E=-A(dB)/(dt) =-(0.0095)*(0.16)=-0.00152V$

The negative indicates the direction of E.

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The wind-chill index is modeled by the function W = 13.12 + 0.6215T − 11.37v0.16 + 0.3965Tv0.16 where T is the temperature (°C) and v is the wind speed (km/h). When T = 12°C and v = 18 km/h, by how much would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Round your answers to two decimal places.)

Answers

This question involves the concepts of derivative, apparent temperature, actual temperature,and wind speed.

The drop in apparent temperature will be "1.25°C".

The apparent temperature (W) is given in terms of actual temperature (T) and wind speed (v) is given by the following function:

$W = 13.12 + 0.6215\ T-11.37\ v^(0.16)+0.3965\ Tv^(0.16)$

Taking the derivative with respect to actual temperature, we get:

$(dW)/(dT)=0.6215+0.3965\ v^(0.16)\n\n$

where,

dW = drop in apparent temperatures = ?

dT = drop in actual temperature = - 1°C

v = wind speed = 18 km/h

Therefore,

$dW=(-1)(0.6215-0.3965(18)^(0.16))$

dW = - 1.25°C

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Answer:

Δw=1.25°C

Explanation:

Given that

$w=13.12 +0.6215 T-11.37 v^(0.16)+0.3965 T v^(0.16)$

Given that T= 12°C and v=19 km/h

Now to find the drop in the apparent temperature w

$(dw)/(dT)=0.6215 +0.3965v^(0.16)$

$(\Delta w)/(\Delta T)= 0.6215 +0.3965 v^(0.16)$

Now by putting the values v=19 km/hr and ΔT=1

$(\Delta w)/(1)=0.6215 +0.3965* 18^(0.16)$

Δw=1.25°C

So we can say that when temperature is decrease by 1°C then apparent temperature will decrease by 1.25°C at given velocity.

Draw a ray diagram for an object placed more than two focal lengths in front of a converging lens.

Answers

Answer:

Explanation:

There is a convex lens M N is placed. An object AB is placed at a distance more than two focal lengths of the lens.

A ray of light is starting from point A and parallel to the principal axis, then after refraction it goes from the focus.

Another ray which goes through the optical centre of the lens becomes undeviated after refraction.

The two refracted rays meet at the point A', So A'B is the image of AB.

The nature of image is real, inverted and diminished.

An electron in a vacuum chamber is fired with a speed of 7400 km/s toward a large, uniformly charged plate 75 cm away. The electron reaches a closest distance of 15 cm before being repelled. What is the plate's surface charge density?

Answers

Answer:

2.29e-9C/m²

Explanation:

Using E = σ/ε₀ means the force on the electron is F = eE = eσ/ε₀.

The work done on the electron is W = Fd = deσ/ε₀. This equals the kinetic energy lost, ½mv².

½mv² = deσ/ε₀

d = 75cm – 15cm = 60cm = 0.6m

σ = mv²ε₀/(2de)

. .= 9.11e-31 * (7.4e6)² * 8.85e-12 / (2 * 0.6 * 1.6e-19)

. .= 2.29e-9 C/m² (i.e. 2.29x10^-9 C/m²)

A body with initial velocity 8.0 m/s moves along a straight line with constant acceleration and travels640 m in 40 s. For the 40 s interval, find (a) the average velocity, (b) the final velocity, and (c) the
acceleration.

Answers

Answer:

(a) The average velocity is 16 m/s

(b) The acceleration is 0.4 m/s^2

(c) The final velocity is 24 m/s

Explanation:

Constant Acceleration Motion

It's a type of motion in which the velocity (or the speed) of an object changes by an equal amount in every equal period of time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, final speed is calculated as follows:

$v_f=v_o+at\qquad\qquad [1]$

The distance traveled by the object is given by:

$\displaystyle x=v_o.t+(a.t^2)/(2)\qquad\qquad [2]$

(a) The average velocity is defined as the total distance traveled divided by the time taken to travel that distance.

We know the distance is x=640 m and the time taken t= 40 s, thus:

$\displaystyle \bar v=(x)/(t)=(640)/(40)=16$

The average velocity is 16 m/s

Using the equation [1] we can solve for a:

$\displaystyle a=(v_f-v_o)/(t)$

$\displaystyle a= 2(x-v_ot)/(t^2)$

Since vo=8 m/s, x=640 m, t=40 s:

$\displaystyle a= 2(640-8\cdot 40)/(40^2)=0.4$

The acceleration is 0.4 m/s^2

(b) The final velocity is calculated by [1]:

$v_f=8+0.4\cdot 40$

$v_f=8+16=24$

The final velocity is 24 m/s

Final answer:

The average velocity is 16 m/s, the final velocity is 8.0 m/s + (acceleration * 40 s), and the acceleration can be found by solving the equation 640 m = (8.0 m/s * 40 s) + (0.5 * acceleration * (40 s)^2.

Explanation:

To find the average velocity, we use the formula: average velocity = total displacement / total time. In this case, the total displacement is 640 m and the total time is 40 s, so the average velocity is 640 m / 40 s = 16 m/s.

To find the final velocity, we can use the formula: final velocity = initial velocity + (acceleration * time). In this case, the initial velocity is 8.0 m/s and the time is 40 s. Since the question states that it moves with constant acceleration, we can assume that the acceleration is the same throughout the 40 s interval. Therefore, the final velocity is 8.0 m/s + (acceleration * 40 s).

To find the acceleration, we can use the formula: total displacement = (initial velocity * time) + (0.5 * acceleration * time^2). In this case, the total displacement is 640 m, the initial velocity is 8.0 m/s, and the time is 40 s. Solving for acceleration, we have 640 m = (8.0 m/s * 40 s) + (0.5 * acceleration * (40 s)^2).

Learn more about Average velocity, Final velocity, Acceleration here:

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Bailey wants to find out which frozen solid melts the fastest: soda, ice, or orange juice. She pours each of the three liquids into the empty cubes of an ice tray, and then places the ice tray in the freezer overnight. The next day, she pulls the ice tray out and sets each cube on its own plate. She then waits and watches for them to melt. When the last part of the frozen liquid melts, she records the time.