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Q. No.A particle having charge \(10^{-9}~\text{C}\) moving in \(x\text-y\) plane in fields of \(0.4\hat{j}~\text{N/C}\) and \(4\times10^{-3}\hat{k}~\text{T}\) experiences a force of \((4 \hat{\imath}+2 \hat{\jmath}) \times 10^{-10} ~\text{N} .\) The velocity of the particle at that instant is: (in m/s)
1. \(50 \hat{i}+100 \hat{j}\)
2. \(100 \hat{i}+50 \hat{j}\)
3. \(-50 \hat{i}+100 \hat{j}\)
4. \(50 \hat{i}-100 \hat{j}\)
1. \(50 \hat{i}+100 \hat{j}\)
2. \(100 \hat{i}+50 \hat{j}\)
3. \(-50 \hat{i}+100 \hat{j}\)
4. \(50 \hat{i}-100 \hat{j}\)
Subtopic: Lorentz Force |
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A current at \(30~\text{A}\) each flows in opposite directions in two conducting wires, placed parallel to each other at a distance \(8~\text{cm}\). The magnetic field at the mid point between the two wires is: (in \(\mu\text{T}\)) \(\left[\dfrac{\mu_0}{4\pi}= 10^{-7}~\text{N/A}^2\right]\)
1. \(30\)
2. \(300\)
3. \(150\)
4. \(0.0\)
1. \(30\)
2. \(300\)
3. \(150\)
4. \(0.0\)
Subtopic: Magnetic Field due to various cases |
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Level 1: 80%+
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A moving coil of galvanometer when shunted with \(2~\Omega\) resistance gives a full scale deflection for a current of \(500~\text{mA}\). When a resistance of \(470~\Omega\) is connected in series it gives a full scale deflection for \(10~\text{V}\) potential applied on it. The value of resistance of galvanometer coil is: (in \(\Omega\)
1. \(50\)
2. \(30\)
3. \(70\)
4. \(100\)
1. \(50\)
2. \(30\)
3. \(70\)
4. \(100\)
Subtopic: Conversion to Ammeter & Voltmeter |
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Level 2: 60%+
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A small cube of side \(1~\text{mm}\) is placed at the centre of a circular loop of radius \(10~\text{cm}\) carrying a current of \(2~\text{A}\). The magnetic energy stored inside the cube is \(\alpha \times 10^{-14} ~\text{J} .\) The value of \(\alpha\) is:
\(\left(\mu_{0}=4 \pi \times 10^{-7} ~\text{Tm} / \text{A}, \pi=3.14\right)\)
1. \(6.28\)
2. \(6.28 \times 10^{-6}\)
3. \(628\)
4. \(6.28 \times 10^{-4}\)
\(\left(\mu_{0}=4 \pi \times 10^{-7} ~\text{Tm} / \text{A}, \pi=3.14\right)\)
1. \(6.28\)
2. \(6.28 \times 10^{-6}\)
3. \(628\)
4. \(6.28 \times 10^{-4}\)
Subtopic: Magnetic Field due to various cases |
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Level 3: 35%-60%
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Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres \(P\) and \(Q\) of a semi circular arc are \(B_1\) and \(B_2\) respectively, Then the ratio \(\dfrac{B_1}{B_2}\) is:
1. \(\dfrac{2+\pi}{1+\pi}\)
2. \(\dfrac{1+\pi}{1-\pi}\)
3. \(\dfrac{2+\pi}{1-\pi}\)
4. \(\dfrac{1+\pi}{2-\pi}\)
1. \(\dfrac{2+\pi}{1+\pi}\)
2. \(\dfrac{1+\pi}{1-\pi}\)
3. \(\dfrac{2+\pi}{1-\pi}\)
4. \(\dfrac{1+\pi}{2-\pi}\)
Subtopic: Magnetic Field due to various cases |
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\(1~\mu\text{C}\) charge moving with velocity \(\vec{v}=(\hat{i}-2 \hat{j}+3 \hat{k})~ \text{m/s}\) in the region of magnetic field \(\overrightarrow{{B}}=(2 \hat{i}+3 \hat{j}-5 \hat{k})~ \text{T}\). The magnitude of forces acting on it is \(\sqrt{\alpha} \times 10^{-6} ~\text{N} .\) The value of \(\alpha\) is:
1. \(151\)
2. \(161\)
3. \(171\)
4. \(180\)
1. \(151\)
2. \(161\)
3. \(171\)
4. \(180\)
Subtopic: Lorentz Force |
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Level 2: 60%+
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The charged particle moving in a uniform magnetic field of \((3 \hat{i}+2 \hat{j})~\text{T}\) has an acceleration \(\left(4 \hat{i}-\dfrac{x}{2} \hat{j}\right) \text{m/s}^2 .\) The value of \(x\) is:
1. \(3\)
2. \(4\)
3. \(8\)
4. \(12\)
1. \(3\)
2. \(4\)
3. \(8\)
4. \(12\)
Subtopic: Lorentz Force |
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A \(5~\text{mg}\) particle carrying a charge of \(5 \pi \times 10^{-6} ~\text{C}\) \((3 \hat{i}+2 \hat{k}) \times 10^{-2} ~\text{m/s}\) \(\vec{B}=0.1 \hat{k}~ \text{Wb/m}^2.\) \(\alpha\) \(\alpha\)
1. \(2\)
2. \(5\)
3. \(7\)
4. \(9\)
1. \(2\)
2. \(5\)
3. \(7\)
4. \(9\)
Subtopic: Lorentz Force |
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Level 2: 60%+
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A voltmeter with internal resistance of \(x~\Omega\) can used to measure upto \(20~\text{V}\). In order to increase its measuring range to \(30~\text{V}\), the required modification is to:
| 1. | connect resistor of \(\dfrac{x}{2}\Omega\), in series with voltmeter |
| 2. | connect resistor of \(\dfrac{x}{2}\Omega\), in parallel to voltmeter |
| 3. | connect resistor of \(x~\Omega\) in series with voltmeter |
| 4. | connect resistor of \(2x~\Omega\) in parallel to voltmeter |
Subtopic: Conversion to Ammeter & Voltmeter |
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Level 2: 60%+
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An insulated wire is wound so that it forms a flat coil with \(N=200\) turns. The radius of the innermost turns is \(r_1=3~\text{cm}\), and of the outermost turn \(r_2=6~\text{cm}\). If \(20~\text{mA}\) current flows in it then the magnetic moment will be \(\alpha\times10^{-2}~\text{Am}^2\). The value of \(\alpha\) is:
1. \(4.4\)
2. \(2.64\)
3. \(3.25\)
4. \(1.2\)
1. \(4.4\)
2. \(2.64\)
3. \(3.25\)
4. \(1.2\)
Subtopic: Magnetic Moment |
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Level 3: 35%-60%
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