Question

A simple generator has a 300 loop square coil of side 20 cm turning in a field of 0.7 T. How fast must it turn to produce a peak output of 210 V?​

Answer 1

Given :

• Number of loops = 300
• Length of the coil = 20 cm
• Magnetic field = 0.7 T
• EMF induced = 210 V

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To find :

• Velocity of the coil to produce a peak output of 210 V.

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Formula to be used :

$\bf\:\maltese$ $\bf\color{black}{\:ε_{ind}~=~VBL}$

‎where,

• $\sf\:ε_{ind}$ denotes emf induced
• L denotes length of the coil
• B denotes the magnetic field

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Solution :

In the question it is mentioned that there are 300 loops so we need to modify the formula and multiply it with N which is equal to number of loops.

‎Therefore,

$\sf\:ε_{ind}~=~N(VBL)$

Substituting the given values

$\sf\longrightarrow\:210~=~300(V \times 0.7 \times 20)$

$\sf\longrightarrow\:210~=~300(V \times \frac{7}{10} \times 20)$

$\sf\longrightarrow\:210~=~300(V \times \frac{140}{10})$

$\sf\longrightarrow\:210~=~300(V \times \frac{14\cancel{0}}{1\cancel{0}})$

$\sf\longrightarrow\:210~=~300(V \times 14)$

$\sf\longrightarrow\:210~=~300 \times 14 \times V$

$\sf\longrightarrow\:\frac{210}{300 \times 14}~=~V$

$\sf\longrightarrow\:\frac{21\cancel{0}}{30\cancel{0} \times 14}~=~V$

$\sf\longrightarrow\:\frac{21}{30 \times 14}~=~V$

$\sf\longrightarrow\:\frac{\cancel{21}}{30 \times \cancel{14}}~=~V$

$\sf\longrightarrow\:\frac{3}{30 \times 2}~=~V$

$\sf\longrightarrow\:\frac{\cancel{3}}{\cancel{30} \times 2}~=~V$

$\sf\longrightarrow\:\frac{1}{10 \times 2}~=~V$

$\sf\longrightarrow\:\frac{1}{20}~=~V$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:V~=~0.05~m/s}}}}$

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Verification :

Let's verify our result with the formula.

$\sf\:ε_{ind}~=~N(VBL)$

$\sf\to\:210~=~300(0.05 \times 0.7 \times 20)$

$\sf\to\:210~=~300(\frac{5}{100} \times \frac{7}{10} \times 20)$

$\sf\to\:210~=~300(\frac{35}{1000} \times 20)$

$\sf\to\:210~=~300(\frac{700}{1000})$

$\sf\to\:210~=~300(\frac{7\cancel{00}}{10\cancel{00}})$

$\sf\to\:210~=~300(\frac{7}{10})$

$\sf\to\:210~=~\frac{2100}{10}$

$\sf\to\:210~=~\frac{210\cancel{0}}{1\cancel{0}}$

$\sf\to\:210~=~210$

Hence Verified !~

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Note : I have explained simple calculations as well therefore it's looking‎ long you can escape some of the steps . Using the formula it has got very short calculation !

:D

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Answer 2

Answer:

Number of loops = 300

Length of the coil = 20 cm

Magnetic field = 0.7 T

EMF induced = 210 V

Explanation:

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