Question:
A solenoid having length 30 cm. If there are 10 turns/cm and current through solenoid changes from 2A to 4A in 3.14 sec. Find emf induced. (Area is A)
A solenoid having length 30 cm. If there are 10 turns/cm and current through solenoid changes from 2A to 4A in 3.14 sec. Find emf induced. (Area is A)
Updated On: Apr 13, 2026
- \(0.24\,A\ \text{volt}\)
- \(0.40\,A\ \text{volt}\)
- \(0.80\,A\ \text{volt}\)
- \(0.20\,A\ \text{volt}\)
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The Correct Option is A
Solution and Explanation
Concept:
Induced emf in a coil is given by
\[
\varepsilon = L \frac{di}{dt}
\]
where \(L\) is the inductance of the solenoid.
For a long solenoid
\[
L = \mu_0 n^2 A \ell
\]
where
\[
n = \text{turns per unit length}, \quad
A = \text{area}, \quad
\ell = \text{length of solenoid}
\]
Step 1:Convert given quantities to SI units. \[ \ell = 30\,\text{cm} = 0.3\,\text{m} \] \[ n = 10\,\text{turns/cm} = 1000\,\text{turns/m} \] Total turns \[ N = n\ell = 1000 \times 0.3 = 300 \]
Step 2:Calculate rate of change of current. \[ \frac{di}{dt} = \frac{4-2}{3.14} \] \[ \frac{di}{dt} = \frac{2}{3.14} \]
Step 3:Find inductance of the solenoid. \[ L = \mu_0 n^2 A \ell \] \[ L = (4\pi \times 10^{-7})(1000)^2 A (0.3) \] \[ L = 1.2\pi \times 10^{-1} A \,H \]
Step 4:Calculate induced emf. \[ \varepsilon = L \frac{di}{dt} \] \[ \varepsilon = (1.2\pi \times 10^{-1}A)\left(\frac{2}{3.14}\right) \] \[ \varepsilon \approx 0.24A \ \text{volt} \] \[ \boxed{\varepsilon = 0.24A \ \text{volt}} \]
Step 1:Convert given quantities to SI units. \[ \ell = 30\,\text{cm} = 0.3\,\text{m} \] \[ n = 10\,\text{turns/cm} = 1000\,\text{turns/m} \] Total turns \[ N = n\ell = 1000 \times 0.3 = 300 \]
Step 2:Calculate rate of change of current. \[ \frac{di}{dt} = \frac{4-2}{3.14} \] \[ \frac{di}{dt} = \frac{2}{3.14} \]
Step 3:Find inductance of the solenoid. \[ L = \mu_0 n^2 A \ell \] \[ L = (4\pi \times 10^{-7})(1000)^2 A (0.3) \] \[ L = 1.2\pi \times 10^{-1} A \,H \]
Step 4:Calculate induced emf. \[ \varepsilon = L \frac{di}{dt} \] \[ \varepsilon = (1.2\pi \times 10^{-1}A)\left(\frac{2}{3.14}\right) \] \[ \varepsilon \approx 0.24A \ \text{volt} \] \[ \boxed{\varepsilon = 0.24A \ \text{volt}} \]
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