Question

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?​

Answer 1

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

$j = \frac{i}{A}$

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

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