Coulomb's Law
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PHXII01:ELECTRIC CHARGES AND FIELDS

358078 An electron moving around the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \(\overrightarrow F \) between the two is (where \(K = \frac{1}{{4\pi {\varepsilon _0}}}\))

1 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\overrightarrow r \)
3 \( - K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \(K\frac{{{e^2}}}{{{r^4}}}\overrightarrow r \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358079 Two identical beads each having a mass \({m}\) and charge \({q}\). When placed in a hemispherical bowl of radius \({R}\) with frictionless, non-conducting walls, the beads move, and at equilibrium they are a distance \({R}\) apart (see figure). If the charge on each bead is found to be \({q=\left[\left(\dfrac{4 \pi \varepsilon_{0} m g R}{\sqrt{N}}\right)^{1 / 2}\right]}\), find the value of \({N}\).
supporting img

1 3
2 7
3 5
4 9
PHXII01:ELECTRIC CHARGES AND FIELDS

358080 Two spheres of electric charges \( + 2\,nC\) and \( - 8\,nC\) are placed at a distance \(d\) apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

1 \(\frac{d}{2}\)
2 \(d\)
3 \(\frac{{3d}}{4}\)
4 \(\frac{{4d}}{3}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358081 Two charges \({Q_1}\) and \({Q_2}\) are present as shown.Two dielectrics of thickness \({t_1}\) and \({t_2}\) and dielectric constants \({k_1}\) and \({k_2}\) are introduced as shown. Find the force between the charges
supporting img

1 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
2 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + {k_1}{t_1} + {k_2}{t_2}} \right]}^2}}}\)
3 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
4 Zero
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PHXII01:ELECTRIC CHARGES AND FIELDS

358078 An electron moving around the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \(\overrightarrow F \) between the two is (where \(K = \frac{1}{{4\pi {\varepsilon _0}}}\))

1 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\overrightarrow r \)
3 \( - K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \(K\frac{{{e^2}}}{{{r^4}}}\overrightarrow r \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358079 Two identical beads each having a mass \({m}\) and charge \({q}\). When placed in a hemispherical bowl of radius \({R}\) with frictionless, non-conducting walls, the beads move, and at equilibrium they are a distance \({R}\) apart (see figure). If the charge on each bead is found to be \({q=\left[\left(\dfrac{4 \pi \varepsilon_{0} m g R}{\sqrt{N}}\right)^{1 / 2}\right]}\), find the value of \({N}\).
supporting img

1 3
2 7
3 5
4 9
PHXII01:ELECTRIC CHARGES AND FIELDS

358080 Two spheres of electric charges \( + 2\,nC\) and \( - 8\,nC\) are placed at a distance \(d\) apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

1 \(\frac{d}{2}\)
2 \(d\)
3 \(\frac{{3d}}{4}\)
4 \(\frac{{4d}}{3}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358081 Two charges \({Q_1}\) and \({Q_2}\) are present as shown.Two dielectrics of thickness \({t_1}\) and \({t_2}\) and dielectric constants \({k_1}\) and \({k_2}\) are introduced as shown. Find the force between the charges
supporting img

1 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
2 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + {k_1}{t_1} + {k_2}{t_2}} \right]}^2}}}\)
3 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
4 Zero
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PHXII01:ELECTRIC CHARGES AND FIELDS

358078 An electron moving around the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \(\overrightarrow F \) between the two is (where \(K = \frac{1}{{4\pi {\varepsilon _0}}}\))

1 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\overrightarrow r \)
3 \( - K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \(K\frac{{{e^2}}}{{{r^4}}}\overrightarrow r \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358079 Two identical beads each having a mass \({m}\) and charge \({q}\). When placed in a hemispherical bowl of radius \({R}\) with frictionless, non-conducting walls, the beads move, and at equilibrium they are a distance \({R}\) apart (see figure). If the charge on each bead is found to be \({q=\left[\left(\dfrac{4 \pi \varepsilon_{0} m g R}{\sqrt{N}}\right)^{1 / 2}\right]}\), find the value of \({N}\).
supporting img

1 3
2 7
3 5
4 9
PHXII01:ELECTRIC CHARGES AND FIELDS

358080 Two spheres of electric charges \( + 2\,nC\) and \( - 8\,nC\) are placed at a distance \(d\) apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

1 \(\frac{d}{2}\)
2 \(d\)
3 \(\frac{{3d}}{4}\)
4 \(\frac{{4d}}{3}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358081 Two charges \({Q_1}\) and \({Q_2}\) are present as shown.Two dielectrics of thickness \({t_1}\) and \({t_2}\) and dielectric constants \({k_1}\) and \({k_2}\) are introduced as shown. Find the force between the charges
supporting img

1 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
2 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + {k_1}{t_1} + {k_2}{t_2}} \right]}^2}}}\)
3 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
4 Zero
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PHXII01:ELECTRIC CHARGES AND FIELDS

358078 An electron moving around the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \(\overrightarrow F \) between the two is (where \(K = \frac{1}{{4\pi {\varepsilon _0}}}\))

1 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\overrightarrow r \)
3 \( - K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \(K\frac{{{e^2}}}{{{r^4}}}\overrightarrow r \)
PHXII01:ELECTRIC CHARGES AND FIELDS

358079 Two identical beads each having a mass \({m}\) and charge \({q}\). When placed in a hemispherical bowl of radius \({R}\) with frictionless, non-conducting walls, the beads move, and at equilibrium they are a distance \({R}\) apart (see figure). If the charge on each bead is found to be \({q=\left[\left(\dfrac{4 \pi \varepsilon_{0} m g R}{\sqrt{N}}\right)^{1 / 2}\right]}\), find the value of \({N}\).
supporting img

1 3
2 7
3 5
4 9
PHXII01:ELECTRIC CHARGES AND FIELDS

358080 Two spheres of electric charges \( + 2\,nC\) and \( - 8\,nC\) are placed at a distance \(d\) apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

1 \(\frac{d}{2}\)
2 \(d\)
3 \(\frac{{3d}}{4}\)
4 \(\frac{{4d}}{3}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358081 Two charges \({Q_1}\) and \({Q_2}\) are present as shown.Two dielectrics of thickness \({t_1}\) and \({t_2}\) and dielectric constants \({k_1}\) and \({k_2}\) are introduced as shown. Find the force between the charges
supporting img

1 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
2 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + {k_1}{t_1} + {k_2}{t_2}} \right]}^2}}}\)
3 \(\frac{{{Q_1}{Q_2}}}{{4\pi {\varepsilon _0}{{\left[ {d - ({t_1} + {t_2}) + \sqrt {{k_1}} {t_1} + \sqrt {{k_2}} {t_2}} \right]}^2}}}\)
4 Zero
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