TS EAMCET · Physics · Magnetic Effects of Current
A solenoid of length 50 cm and radius 10 cm has two closely wound layers of windings 100 turns each. If a current of 2.5 A is passing through the windings, the magnetic field (in \(10^{-4} \mathrm{~T}\) ) at a point 5 cm from the axis is
- A \(2 \pi\)
- B \(31.4\)
- C \(4 \pi\)
- D Zero
Answer & Solution
Correct Answer
(C) \(4 \pi\)
Step-by-step Solution
Detailed explanation
\(N = 2 \times 100 = 200\) \(n = \frac{N}{L} = \frac{200}{0.5 \mathrm{~m}} = 400 \mathrm{~m^{-1}}\) \(B = \mu_0 n I = (4 \pi \times 10^{-7} \mathrm{~T \cdot m/A})(400 \mathrm{~m^{-1}})(2.5 \mathrm{~A}) = 4 \pi \times 10^{-4} \mathrm{~T}\) The magnetic field in…
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Momentum before collision,
\(
p_1=4 m v_1-2 m v_2
\)
Momentum after collision,
\(
p_2=6 m\left(-5 v_2\right)=-30 m v_2
\)
Conservation of momentum gives,
\(
\begin{gathered}
p_1=p_2 \\
\Rightarrow \quad 4 m v_1-2 m v_2=-30 m v_2 \quad \Rightarrow 4 v_1=-32 v_2 \\
\Rightarrow \quad \frac{v_1}{v_2}=\frac{-32}{4}=-8 \text { or }\left|\frac{v_1}{v_2}\right|=8
\end{gathered}
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