Electrostatics & Capacitors · JEE Main previous year questions

2017 7 questions

1. Q402017 · 9 Apr 2017 · Shift 1

   The electric field component of a monochromatic radiation is given by $\vec{E}=2{\mathrm{E}}_0\hat{i}\cos kz\cos \omega t$ Its magnetic field $\vec{B}$ is then given by :

   1. A.$\frac{2E_0}{c}\hat{j}\sin kz\cos \omega t$
   2. B.$-\frac{2E_0}{c}\hat{j}\sin kz\sin \omega t$
   3. C.$\frac{2E_0}{c}\hat{j}\sin kz\sin \omega t$
   4. D.$\frac{2E_0}{c}\hat{j}\cos kz\cos \omega t$
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   Answer: C

2. Q532017 · 9 Apr 2017 · Shift 1
   
   1. A.${\Phi }_1<{\Phi }_2={\Phi }_3>{\Phi }_4$
   2. B.${\Phi }_1>{\Phi }_2>{\Phi }_3>{\Phi }_4$
   3. C.${\Phi }_1={\Phi }_2={\Phi }_3={\Phi }_4$
   4. D.${\Phi }_1>{\Phi }_3;{\Phi }_2<{\Phi }_4$
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   Answer: C

3. Q542017 · 9 Apr 2017 · Shift 1
   
   1. A.$3$
   2. B.$4$
   3. C.$5$
   4. D.$6$
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   Answer: C

4. Q412017 · 8 Apr 2017 · Shift 1

   There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of $60^{\circ }$ with the direction of the field ?

   1. A.$589.5\mathrm{V}$
   2. B.$589.2\mathrm{V}$
   3. C.$589.4\mathrm{V}$
   4. D.$589.6\mathrm{V}$
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   Answer: B

5. Q422017 · 8 Apr 2017 · Shift 1

   The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains $4\mu \mathrm{C}$ charge, its radius will be : [ Take : $\frac{1}{4\pi {ϵ}_0}=9\times 10^9\mathrm{N}-{\mathrm{m}}^2/{\mathrm{C}}^2$ ]

   1. A.$20\mathrm{mm}$
   2. B.$32\mathrm{mm}$
   3. C.$28\mathrm{mm}$
   4. D.$16\mathrm{mm}$
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   Answer: D

6. Q432017 · 8 Apr 2017 · Shift 1

   In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec{B}=B_0\left(\hat{i}+2\hat{j}-4\hat{k}\right)$. If a test charge moving with a velocity $\vec{v}=v_0\left(3\hat{i}-\hat{j}+2\hat{k}\right)$ experiences no force in that region, then the electric field in the region, in SI units, is :

   1. A.$\vec{E}=-v_0{B}_0\left(3\hat{i}-2\hat{j}-4\hat{k}\right)$
   2. B.$\vec{E}=-v_0{B}_0\left(\hat{i}+\hat{j}+7\hat{k}\right)$
   3. C.$\vec{E}=v_0{B}_0\left(14\hat{j}+7\hat{k}\right)$
   4. D.$\vec{E}=-v_0{B}_0\left(14\hat{j}+7\hat{k}\right)$
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   Answer: D

7. Q492017 · 8 Apr 2017 · Shift 1

   Magnetic field in a plane electromagnetic wave is given by $\vec{B}={\mathrm{B}}_0\sin (k\mathrm{x}+\omega t)\hat{j}T$ Expression for corresponding electric field will be : Where c is speed of light.

   1. A.$\vec{E}={\mathrm{B}}_0\mathrm{c}\sin (k\mathrm{x}+\omega t)\hat{k}V/m$
   2. B.$\vec{E}=\frac{B_0}{c}\sin (k\mathrm{x}+\omega t)\hat{k}V/m$
   3. C.$\vec{E}=-{\mathrm{B}}_0\mathrm{c}\sin (\mathrm{kx}+\omega t)\hat{k}V/m$
   4. D.$\vec{E}={\mathrm{B}}_0\mathrm{c}\sin (\mathrm{kx}-\omega t)\hat{k}V/m$
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   Answer: A