Electric Dipole
PHXII01:ELECTRIC CHARGES AND FIELDS

358138 Two point charges of \(5\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 5\mu C\) are separated by a distance of \(10\,\mathop A\limits^ \circ \), \(A\) point \(B\) is at a distance of 10 \(cm\) from the midpoint and on the perpendicular bisector of the line joining the two charges. The electric field at \(B \) will be

1 \(5\,\,N\,{C^{ - 1}}\)
2 \(0.9\,\,N\,{C^{ - 1}}\)
3 \(45\,N\,{C^{ - 1}}\)
4 \(0.045\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358139 In the situation shown in the diagram, magnitude of \(q < < |Q|\) and \(r>>a\). The net force on the free charge \(-q\) and net torque on it about \(O\) at the instant shown are respectively \([p = 2aQ\) is the dipole moment]
supporting img

1 \(-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
2 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},+\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
3 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
4 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}, \dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358140 What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

1 \(0^\circ \)
2 \(90^\circ \)
3 \(180^\circ \)
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358141 Two charges \( + 10\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 10\mu C\) are placed 20 \(mm\) apart. The electric field at point \(P\), on the axis of the dipole 100 \(cm\) away from its centre \(O\) on the side of the positive charge is
supporting img

1 \(9 \times {10^9}\,\,N{C^{ - 1}}\)
2 \(4.2 \times {10^6}\,\,N{C^{ - 1}}\)
3 \(3.6 \times {10^3}\,\,N{C^{ - 1}}\)
4 \(3.6 \times {10^5}\,\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358138 Two point charges of \(5\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 5\mu C\) are separated by a distance of \(10\,\mathop A\limits^ \circ \), \(A\) point \(B\) is at a distance of 10 \(cm\) from the midpoint and on the perpendicular bisector of the line joining the two charges. The electric field at \(B \) will be

1 \(5\,\,N\,{C^{ - 1}}\)
2 \(0.9\,\,N\,{C^{ - 1}}\)
3 \(45\,N\,{C^{ - 1}}\)
4 \(0.045\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358139 In the situation shown in the diagram, magnitude of \(q < < |Q|\) and \(r>>a\). The net force on the free charge \(-q\) and net torque on it about \(O\) at the instant shown are respectively \([p = 2aQ\) is the dipole moment]
supporting img

1 \(-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
2 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},+\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
3 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
4 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}, \dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358140 What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

1 \(0^\circ \)
2 \(90^\circ \)
3 \(180^\circ \)
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358141 Two charges \( + 10\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 10\mu C\) are placed 20 \(mm\) apart. The electric field at point \(P\), on the axis of the dipole 100 \(cm\) away from its centre \(O\) on the side of the positive charge is
supporting img

1 \(9 \times {10^9}\,\,N{C^{ - 1}}\)
2 \(4.2 \times {10^6}\,\,N{C^{ - 1}}\)
3 \(3.6 \times {10^3}\,\,N{C^{ - 1}}\)
4 \(3.6 \times {10^5}\,\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358138 Two point charges of \(5\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 5\mu C\) are separated by a distance of \(10\,\mathop A\limits^ \circ \), \(A\) point \(B\) is at a distance of 10 \(cm\) from the midpoint and on the perpendicular bisector of the line joining the two charges. The electric field at \(B \) will be

1 \(5\,\,N\,{C^{ - 1}}\)
2 \(0.9\,\,N\,{C^{ - 1}}\)
3 \(45\,N\,{C^{ - 1}}\)
4 \(0.045\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358139 In the situation shown in the diagram, magnitude of \(q < < |Q|\) and \(r>>a\). The net force on the free charge \(-q\) and net torque on it about \(O\) at the instant shown are respectively \([p = 2aQ\) is the dipole moment]
supporting img

1 \(-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
2 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},+\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
3 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
4 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}, \dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358140 What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

1 \(0^\circ \)
2 \(90^\circ \)
3 \(180^\circ \)
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358141 Two charges \( + 10\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 10\mu C\) are placed 20 \(mm\) apart. The electric field at point \(P\), on the axis of the dipole 100 \(cm\) away from its centre \(O\) on the side of the positive charge is
supporting img

1 \(9 \times {10^9}\,\,N{C^{ - 1}}\)
2 \(4.2 \times {10^6}\,\,N{C^{ - 1}}\)
3 \(3.6 \times {10^3}\,\,N{C^{ - 1}}\)
4 \(3.6 \times {10^5}\,\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358138 Two point charges of \(5\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 5\mu C\) are separated by a distance of \(10\,\mathop A\limits^ \circ \), \(A\) point \(B\) is at a distance of 10 \(cm\) from the midpoint and on the perpendicular bisector of the line joining the two charges. The electric field at \(B \) will be

1 \(5\,\,N\,{C^{ - 1}}\)
2 \(0.9\,\,N\,{C^{ - 1}}\)
3 \(45\,N\,{C^{ - 1}}\)
4 \(0.045\,N{C^{ - 1}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358139 In the situation shown in the diagram, magnitude of \(q < < |Q|\) and \(r>>a\). The net force on the free charge \(-q\) and net torque on it about \(O\) at the instant shown are respectively \([p = 2aQ\) is the dipole moment]
supporting img

1 \(-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
2 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},+\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
3 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i},-\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}\)
4 \(\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{2}} \hat{k}, \dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{p q}{r^{3}} \hat{i}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358140 What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

1 \(0^\circ \)
2 \(90^\circ \)
3 \(180^\circ \)
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358141 Two charges \( + 10\mu C\,\,\,{\mathop{\rm and}\nolimits} \,\,\, - 10\mu C\) are placed 20 \(mm\) apart. The electric field at point \(P\), on the axis of the dipole 100 \(cm\) away from its centre \(O\) on the side of the positive charge is
supporting img

1 \(9 \times {10^9}\,\,N{C^{ - 1}}\)
2 \(4.2 \times {10^6}\,\,N{C^{ - 1}}\)
3 \(3.6 \times {10^3}\,\,N{C^{ - 1}}\)
4 \(3.6 \times {10^5}\,\,N{C^{ - 1}}\)