A wire 48 m long carries a current of 18 A from west to east.

Mathematics

1 answer:

Arisa [49]3 years ago

4 0

Step-by-step explanation:

Given that,

The length of a wire, L = 48 m

Current in the wire, I = 18 A (west to east)

The magnetic field in the wire, B = $8.3\times 10^4\ T$ (towards south)

The magnetic force acting on the wire is given by :

$F=I(L\times B)\\\\F=48\cdot18\cdot8.3\cdot10^{-4}\ N\\\\F=0.71\ N$

Using right hand rule, the direction of magnetic force is upwards.

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Find (a) arc length and (b) Area of a sector.

barxatty [35]

Answer:

a) 29.45 cm (2 dp)

b) 220.89 cm² (2 dp)

Step-by-step explanation:

Formula

$\textsf{Arc length}=r \theta$

$\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta$

$\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}$

Calculation

Given:

$\theta=\dfrac{5 \pi}{8}$
r = 15 cm

$\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}$

$\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}$