Moving Charges and Magnetism

1. A.
   $\frac{m_1}{m_2} > \frac{q_1}{q_2}$
2. B.
   $\frac{m_1}{m_2} > \frac{q_2}{q_1}$
3. C.
   $\frac{m_1}{m_2} < \frac{q_1}{q_2}$
4. D.
   $\frac{m_1}{m_2} < \frac{q_2}{q_1}$

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1. A.
   $\dfrac{\mu_0 I}{\pi a}$ and directed along OC
2. B.
   $\dfrac{\mu_0 I}{\pi a \sqrt{2}}$ and directed along OD
3. C.
   $\dfrac{\mu_0 I \sqrt{2}}{\pi a}$ and directed along OB
4. D.
   $\dfrac{2 \mu_0 I}{\pi a}$ and directed along OA

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1. A.
   Zero
2. B.
   $\frac{\mu_0 I}{2\pi a}$
3. C.
   $\frac{\mu_0 I}{4\pi a}$
4. D.
   $\frac{\mu_0 I}{6\pi a}$

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1. A.
   z-axis
2. B.
   $-z$-axis
3. C.
   $x$-axis
4. D.
   $-x$-axis

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1. A.
2. B.
3. C.
4. D.

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1. A.
   South
2. B.
   East
3. C.
   West
4. D.
   North

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1. A.
   10 mA
2. B.
   100 mA
3. C.
   1 mA
4. D.
   3 mA

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1. A.
   $\dfrac{\mathrm{KB}^2}{2\mathrm{E}^2}$
2. B.
   $\dfrac{2\mathrm{KB}^2}{\mathrm{E}^2}$
3. C.
   $\dfrac{2\mathrm{KE}^2}{\mathrm{B}^2}$
4. D.
   $\dfrac{\mathrm{KE}^2}{2\mathrm{B}^2}$

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1. A.
   $6 \times 10^{-4}\ \mathrm{Am^2}$
2. B.
   $3 \times 10^{-5}\ \mathrm{Am^2}$
3. C.
   $1{\cdot}5 \times 10^{-4}\ \mathrm{Am^2}$
4. D.
   $5 \times 10^{-5}\ \mathrm{Am^2}$

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1. A.
   $(1\ \mathrm{nT})\ \hat{j}$
2. B.
   $(10\ \mathrm{nT})\ \hat{k}$
3. C.
   $-(10\ \mathrm{nT})\ \hat{k}$
4. D.
   $-(1\ \mathrm{nT})\ \hat{j}$

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1. A.
   y-axis
2. B.
   $-y$-axis
3. C.
   z-axis
4. D.
   $-z$-axis

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1. A.
   $2\pi I$, along +X – axis
2. B.
   $2\pi I$ along –X – axis
3. C.
   $\pi I$ along +X – axis
4. D.
   $\pi I$ along –X – axis

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1. A.
   150 $\Omega$
2. B.
   125 $\Omega$
3. C.
   100 $\Omega$
4. D.
   75 $\Omega$

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Both Assertion (A) and Reason (R) are false.

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1. A.
   use of soft iron core which increases the magnetic field.
2. B.
   radial magnetic field
3. C.
   hair spring which provides the counter torque
4. D.
   eddy current in the iron core which causes damping.

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1. A.
   increasing number of turns of the coil
2. B.
   increasing area of coil and magnitic field strength
3. C.
   decreasing area of coil and magnetic field strength
4. D.
   increasing torsional constant of the hair spring

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1. A.
   1.0 N m
2. B.
   2.0 N m
3. C.
   0.50 N m
4. D.
   0.25 N m

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1. A.
   4015 $\Omega$
2. B.
   3985 $\Omega$
3. C.
   415 $\Omega$
4. D.
   385 $\Omega$

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1. A.
   0.05 $\Omega$ should be connected in series with it.
2. B.
   0.05 $\Omega$ should be connected in parallel with it.
3. C.
   0.01 $\Omega$ should be connected in parallel with it.
4. D.
   0.01 $\Omega$ should be connected in series with it.

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1. A.
   $\dfrac{1}{2}$
2. B.
   $\dfrac{1}{4}$
3. C.
   4
4. D.
   1

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1. A.
   $\dfrac{1}{\sqrt{2}}$
2. B.
   $\sqrt{2}$
3. C.
   $\dfrac{1}{2}$
4. D.
   2

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1. A.
   both particles revolve clockwise
2. B.
   both particles revolve anticlockwise
3. C.
   particle 1 revolves clockwise while particle 2 revolves anticlockwise
4. D.
   particle 1 revolves anticlockwise while particle 2 revolves clockwise

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1. A.
   1 s
2. B.
   2 s
3. C.
   4 s
4. D.
   8 s

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1. A.
   $p_1 = \dfrac{p_2}{2}$
2. B.
   $p_1 = p_2$
3. C.
   $p_1 = 2p_2$
4. D.
   $p_1 = 4p_2$

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1. A.
   $1.0 \times 10^{-9}\,\hat{k}$ T
2. B.
   $-1.0 \times 10^{-9}\,\hat{k}$ T
3. C.
   $\frac{5.0}{\sqrt{2}} \times 10^{-10}\,\hat{k}$ T
4. D.
   $-\frac{5.0}{\sqrt{2}} \times 10^{-10}\,\hat{k}$ T

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1. A.
   $(0{\cdot}12\,\hat{j} - 0{\cdot}16\,\hat{k})$ N
2. B.
   $(-\,0{\cdot}16\,\hat{j} + 0{\cdot}12\,\hat{k})$ N
3. C.
   $(-\,0{\cdot}12\,\hat{j} + 0{\cdot}16\,\hat{k})$ N
4. D.
   $(0{\cdot}16\,\hat{j} - 0{\cdot}12\,\hat{k})$ N

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1. A.
   $qv_0\,(B_1 + B_2)$
2. B.
   $q\sqrt{v_0\,(B_1 + B_2)}$
3. C.
   $q\,v_0\sqrt{(B_1^2 + B_2^2)}$
4. D.
   $q\sqrt{v_0\,(B_1^2 + B_2^2)}$

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1. A.
   $\dfrac{\mu_0 \mathrm{I}}{\mathrm{R}}$
2. B.
   zero
3. C.
   $\dfrac{\mu_0 \mathrm{I}}{2\mathrm{R}}$
4. D.
   $\dfrac{\mu_0 \mathrm{I}}{4\mathrm{R}}$

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1. A.
   x-axis
2. B.
   y-axis
3. C.
   z-axis
4. D.
   negative z-axis

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1. A.
   $\dfrac{\mu_0 I}{2\pi R}$
2. B.
   $\dfrac{\mu_0 I}{\pi R}$
3. C.
   $\dfrac{\mu_0 I}{4R}$
4. D.
   $\dfrac{\mu_0 I}{R}$

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1. A.
   a circular path in XZ plane
2. B.
   a semicircular path in XY plane
3. C.
   a helical path with its axis parallel to Y-axis
4. D.
   a semicircular path in YZ plane

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1. A.
   $(2\hat{j} + 3\hat{k})$ mN
2. B.
   $(-3\hat{j} + 2\hat{k})$ $\mu$N
3. C.
   $(6\hat{j} + 4\hat{k})$ mN
4. D.
   $(-4\hat{j} + 6\hat{k})$ $\mu$N

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1. A.
   $2{\cdot}5$ cm
2. B.
   5 cm
3. C.
   8 cm
4. D.
   10 cm

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1. A.
   $0{\cdot}019\ \mathrm{Am^2}$
2. B.
   $0{\cdot}14\ \mathrm{Am^2}$
3. C.
   $0{\cdot}196\ \mathrm{Am^2}$
4. D.
   $0{\cdot}615\ \mathrm{Am^2}$

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1. A.
   small resistance in series
2. B.
   large resistance in series
3. C.
   small resistance in parallel
4. D.
   large resistance in parallel

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1. A.
   2
2. B.
   $\dfrac{1}{2}$
3. C.
   $\dfrac{1}{4}$
4. D.
   4

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1. A.
   horizontal straight lines directed radially out from the wire.
2. B.
   straight lines parallel to the current-carrying wire.
3. C.
   concentric horizonal circles around the wire.
4. D.
   coaxial helixes around the wire.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Both Assertion (A) and Reason (R) are false.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false and Reason (R) is also false.

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