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Vinil7 [7]
3 years ago
12

A current-carrying wire is bent into a circular loop of radius R and lies in an xy plane. A uniform external magnetic field B in

the +z direction exists throughout the plane of the loop. The current has the magnitude of I and it is deirected counterclockwise when observing from positive z axis.What is the magnetic force exerted by the external field on the loop?
Express your answer in terms of some or all of the variables I, R, and B
Physics
1 answer:
Ilya [14]3 years ago
8 0

Answer:

 F = 2π I R B

Explanation:

The magnetic force is described by the equation.

      F = q v x B = i L  x B

Where i is the current, L is a vector that points in the direction of the current (length) and B is the magnetic field.

This equation can be used in scalar form and the direction of the force found by the right hand ruler, the thumb goes in the direction of L, the fingers extended in the direction of B and the palm of the hand indicates the direction of the force if the load is positive

     F = i L B sin θ

In this case the wire is in the xy plane and the z-axis field whereby they are perpendicular, θ = 90º and sin 90 = 1

     F = i L B

The loop length is

    L = 2π R

    F = i 2π R B

    F = 2π I R B

The force is in the loop

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A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her orig
atroni [7]

Answer:

The plane is 2353.7 mi from the starting position.

Explanation:

Please, see the attached figure for a graphic representation of the problem.

We have 2 displacement vectors "a" and "b" and a vector "c" that is the sum of vectors "a" plus "b" (c = a + b). The module of "c" will be the distance of the plane from the starting point.

vector a = (xa, ya)

vector b = (xb, yb)

where “xa” and “xb” are the horizontal components of the vectors “a” and “b” respectively and “ya” and “yb” are the vertical components of each vector.

Then, the vector c = a + b will be:

c = (xa + xb, ya + yb)

The module of a vector is calculated using the following expression for a vector “v”:

module of v = \sqrt{x^{2} + y^{2} }

Then, the module of c will be:

module of c = \sqrt{(xa + xb)^{2} + (ya + yb)^{2}} = distance from starting point

Then, we have to find the components of vectors “a” and “b”

The distance traveled during the first 1.5 hours of the trip is the module of the vector “a”. Then:

module of a = \sqrt{xa^{2} + ya^{2} } = distance traveled during the first 1.5 hours.

The distance can be calculated using the equation of the position of an object moving in a straight line at constant speed:

x = x0 + v * t

where

x = position at time t

x0 = initial position

v = speed

t = time

Considering x0 as the starting point (x0 = 0)

x = 675 mi/h * 1.5 h = 1012.5 mi

Then:

module of a = \sqrt{xa^{2} + ya^{2} } = 1012. 5 mi

Since the plane moves only on the horizontal (see figure), the "y" component of the vector, "ya", will be 0.

Then:

(1012.5 mi)² = xa²

xa = 1012. 5mi

a = (1012.5 mi, 0)

In the same way, we have fo find the components of the vector “b”. The module of “b” will be the distance traveled during this part of the flight:

module of b = \sqrt{xb^{2} + yb^{2} } = x = x0 + v * t

Considering x0 as the point at which the plane turns (x0 = 0)

x = 675 mi / h * 2 h = 1350 mi

Using trigonometry, we can calculate xb and yb (see figure):

sin angle = opposite / hypotenuse

cos angle = adjacent / hypotenuse

In this case:

opposite = yb

adjacent = xb

hypotenuse = module of “b”

Then:

sin 10° = yb / module of “b”

sin 10° * module of “b” = yb

In the same way:

cos 10° * module of “b” = xb

Since module of “b” = 1350 mi

xb = 1329.5 mi

yb = 234.4 mi

b = (1329.5 mi, 234.4 mi)

The vector c = a+b can now be calculated:

c = (xa + xb, ya + yb)

c =(1012.5 mi + 1329.5 mi, 0 mi + 234.4 mi) = (2342 mi, 234.4 mi)

The module of c will be:

module of c = \sqrt{(2342 mi)^{2} + (234.4 mi)^{2} } = 2353.7 mi

The plane is 2353.7 mi from the starting position.

4 0
3 years ago
Convert 75.0 degrees Fahrenheit into Celsius
nikdorinn [45]

Answer:

23.889 Celcius

Explanation:

(75°F − 32) × 5/9 = 23.889°C

3 0
3 years ago
Read 2 more answers
If the battery of your phone can provide 2 mA of current to your phone and holds a charge of 130 C, how long will it take a full
Naya [18.7K]

Answer: 65000 seconds

Explanation:

Given that,

Current (I) = 2 mA

(Since 1 mA = 1 x 10^-3A

2 mA = 2 x 10^-3A)

Charge (Q) = 130 C

Time taken for a fully charged phone to die (T) = ?

Recall that the charge is the product of current and time taken.

i.e Q = I x T

130C = 2 x 10^-3A x T

T = 130C / (2 x 10^-3A)

T = 65000 seconds (time will be in seconds because seconds is the unit of time)

Thus, it will take a fully charged phone 65000 seconds to die

5 0
3 years ago
If 20 beats are produced within a single second, which of the following frequencies could possibly be held by two sound waves tr
zhuklara [117]

The correct choice is

D. 22 Hz and 42 Hz.

In fact, the beat frequency is given by the difference between the frequencies of the two waves:

f_B = |f_1 -f_2|

In this problem, the beat frequency is f_B=20 Hz, therefore the only pair of frequencies that gives a difference equal to 20 Hz is

D. 22 Hz and 42 Hz.

4 0
3 years ago
Read 2 more answers
________ In many cartoon shows, a character runs off a cliff, realizes his predicament, and lets out a scream. He continues to s
IrinaVladis [17]

Answer:

Here the source is moving away from the observer so frequency will be smaller than the actual frequency and since the speed is increasing so the frequency is decreasing with time so correct answer is

D) lower than the original pitch and decreasing as he falls.

Explanation:

As we know by the Doppler's effect of sound we have

so we will have

f = f_o(\frac{v}{v + v_s})

so here when source moves away from the observer with a some speed then the frequency of the sound observed by the observer is smaller than the actual frequency

Here we know that the speed of the source is increasing with time as the source is falling under gravity

So we can say that the pitch of the sound will decrease with time

4 0
3 years ago
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