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GuDViN [60]
3 years ago
9

6.7.1 Current and Current Density A sphere of radius 10 mm that carries a charge of 8 nC =8x 10°C is whirled in a circle at the

end of an insulated string. The rotation frequency is 100x rad/s. (a) What is the basic definition of current in terms of charge? (b) What average current does this rotating charge represent? (c) What is the average current density over the area traversed by the sphere?​
Physics
1 answer:
aev [14]3 years ago
6 0

Answer:

Part a)

Rate of charge flow is known as electric current

Part b)

Average current flow is

i = 4\times 10^{-7} A

Part c)

As we know that current density is current per unit area

j = 1.27 \times 10^{-3} A/m^2

Explanation:

As we know that angular frequency of rotation is

\omega = 100\pi rad/s

now by basic definition of electric current

Part a)

Rate of charge flow is known as electric current

i = \frac{dq}{dt}

so here we have

i = \frac{Q}{T}

i = Qf

Part b)

here we know that

\omega = 2\pi f

100\pi = 2\pi f

f = 50 Hz

now we have

i = (8\times 10^{-9})(50)

i = 4\times 10^{-7} A

Part c)

As we know that current density is current per unit area

So we have

j = \frac{i}{A}

j = \frac{4\times 10^{-7}}{\pi(10\times 10^{-3})^2}

j = 1.27 \times 10^{-3} A/m^2

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the sum of vectors with the Pythagorean theorem allows us to find that the maximum magnitude occurs for the case:

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Vectors are physical quantities that have modulus and direction, for example: force, velocity, acceleration, etc.

Vector algebra has defined the sum, the product by a scalar and by a vector.  The modulus and the direction of the resulting vector must be encoded.

The sum of two quantities is done using the Pythagorean theorem

                  c² = a² + b²

where c is the resultant called hypotenuse, a and b are the summing vectors called legs; trigonometry is used for the direction.

Let's apply this expression to the present case

a, b) perpendicular vectors

              c² = a² + b²

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              c = 11.7

the magnitude is the same in both cases, changing the direction of the vector

c) Antiparallel vectors

             

For this case the vectors are collinear, so the sum reduces to the algebraic addition

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d) parallel vectors

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We can see that the vectors addition gives their maximum and minimum values ​​when the vectors are collinear.

In conclusion using the vectors addition we find that the correct answer is

d) the two vectors are parallel

learn more about vector addition here:

brainly.com/question/15074838

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