An equilateral triangular loop ADC having some resistance is pulled...

An equilateral triangular loop $ADC$ having some resistance is pulled with a constant velocity

v

out of a uniform magnetic field directed into the screen. At time

t = 0

, side

DC

of the loop is at edge of the magnetic field. The induced current \left(i\right)

versus time \left(t\right)

graph will be as

An equilateral triangular loop ADC having some resistance is pulled with a constant velocity v out of a uniform

Options

Correct answer

B. How many resonating structures does aniline have?

Step-by-step solution

Let 2a be the side of the triangle and b the length AE.

An equilateral triangular loop ADC having some resistance is pulled with a constant velocity v out of a uniform

\dfrac{\text{AH}}{\text{AE}} = \dfrac{\text{GH}}{\text{EC}}

∴ \text{GH} = \left(\dfrac{\text{AH}}{\text{AE}}\right) \text{EC}

\text{GH} = \dfrac{\left(\text{b} - \text{vt}\right)}{\text{b}} \cdot \text{a}

= \text{a} - \left(\dfrac{\text{a}}{\text{b}} \text{vt}\right)

∴ \text{FG} = 2 \text{GH} = 2 \left[\text{a} - \dfrac{\text{a}}{\text{b}} \text{vt}\right]

Induced emf

\text{e} = \text{Bv} \left(\text{FG}\right) = 2 \text{Bv} \left(\text{a} - \dfrac{\text{a}}{\text{b}} \text{vt}\right)

∴

Induced current

\text{i} = \dfrac{\text{e}}{\text{R}} = \dfrac{2 \text{Bv}}{\text{R}} \left[\text{a} - \dfrac{\text{a}}{\text{b}} \text{vt}\right]

or i = k₁ - k₂t

Thus, i-t graph is a straight line with negative slope and positive intercept.

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