Continuous Charge Distribution
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PHXII01:ELECTRIC CHARGES AND FIELDS

358032 A thin semi-circular ring of radius \(r\) has a positive charge \(q\) distributed uniformly over it. The net electric field \(\overrightarrow E \) at the centre \(O\) is
supporting img

1 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
2 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
3 \( - \frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
4 \( - \frac{q}{{4{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358033 A thin conducting ring of radius \(R\) is given a charge + \(Q\). The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E\). The electric field at the centre due to the charge on the part \(ACD\) of the ring is
supporting img

1 \(\sqrt 2 E\,\,{\rm{along}}\,\,OB\)
2 \(\sqrt 2 E\,\,{\rm{along}}\,\,KO\)
3 \(2E\,\,{\rm{along}}\,\,OK\)
4 \(\sqrt 3 E\,\,{\rm{along}}\,\,KO\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358034 A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring as shown in the figure. Then
supporting img

1 If \(q > O\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
2 If \(q < O\) and is displaced away from the centre in the plane of the ring then it will continue moving till it hits the ring.
3 If \(q < O\) will perform SHM for small displacement along the axis.
4 All of the above.
PHXII01:ELECTRIC CHARGES AND FIELDS

358035 A ring of radius \(r\) carries a charge \(Q\) uniformly distributed over its length. A charge \(q\) is placed at its centre will experience a force equal to

1 \(\frac{{qQ}}{{8\pi {\varepsilon _0}{r^3}}}\)
2 \(\frac{{qQ}}{{4\pi {\varepsilon _0}{r^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358036 Charge \(q\) is uniformly distributed over a thin half ring of radius \(R\). The electric field at the centre of the ring is

1 \(\dfrac{q}{2 \pi^{2} \varepsilon_{0} R^{2}}\)
2 \(\dfrac{q}{4 \pi^{2} \varepsilon_{0} R^{2}}\)
3 \(\dfrac{q}{4 \pi \varepsilon_{0} R^{2}}\)
4 \(\dfrac{q}{2 \pi \varepsilon_{0} R^{2}}\)
AIIMS - 2008
NEET DIGITAL LIBRARY
PHXII01:ELECTRIC CHARGES AND FIELDS

358032 A thin semi-circular ring of radius \(r\) has a positive charge \(q\) distributed uniformly over it. The net electric field \(\overrightarrow E \) at the centre \(O\) is
supporting img

1 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
2 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
3 \( - \frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
4 \( - \frac{q}{{4{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358033 A thin conducting ring of radius \(R\) is given a charge + \(Q\). The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E\). The electric field at the centre due to the charge on the part \(ACD\) of the ring is
supporting img

1 \(\sqrt 2 E\,\,{\rm{along}}\,\,OB\)
2 \(\sqrt 2 E\,\,{\rm{along}}\,\,KO\)
3 \(2E\,\,{\rm{along}}\,\,OK\)
4 \(\sqrt 3 E\,\,{\rm{along}}\,\,KO\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358034 A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring as shown in the figure. Then
supporting img

1 If \(q > O\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
2 If \(q < O\) and is displaced away from the centre in the plane of the ring then it will continue moving till it hits the ring.
3 If \(q < O\) will perform SHM for small displacement along the axis.
4 All of the above.
PHXII01:ELECTRIC CHARGES AND FIELDS

358035 A ring of radius \(r\) carries a charge \(Q\) uniformly distributed over its length. A charge \(q\) is placed at its centre will experience a force equal to

1 \(\frac{{qQ}}{{8\pi {\varepsilon _0}{r^3}}}\)
2 \(\frac{{qQ}}{{4\pi {\varepsilon _0}{r^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358036 Charge \(q\) is uniformly distributed over a thin half ring of radius \(R\). The electric field at the centre of the ring is

1 \(\dfrac{q}{2 \pi^{2} \varepsilon_{0} R^{2}}\)
2 \(\dfrac{q}{4 \pi^{2} \varepsilon_{0} R^{2}}\)
3 \(\dfrac{q}{4 \pi \varepsilon_{0} R^{2}}\)
4 \(\dfrac{q}{2 \pi \varepsilon_{0} R^{2}}\)
AIIMS - 2008
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PHXII01:ELECTRIC CHARGES AND FIELDS

358032 A thin semi-circular ring of radius \(r\) has a positive charge \(q\) distributed uniformly over it. The net electric field \(\overrightarrow E \) at the centre \(O\) is
supporting img

1 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
2 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
3 \( - \frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
4 \( - \frac{q}{{4{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358033 A thin conducting ring of radius \(R\) is given a charge + \(Q\). The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E\). The electric field at the centre due to the charge on the part \(ACD\) of the ring is
supporting img

1 \(\sqrt 2 E\,\,{\rm{along}}\,\,OB\)
2 \(\sqrt 2 E\,\,{\rm{along}}\,\,KO\)
3 \(2E\,\,{\rm{along}}\,\,OK\)
4 \(\sqrt 3 E\,\,{\rm{along}}\,\,KO\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358034 A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring as shown in the figure. Then
supporting img

1 If \(q > O\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
2 If \(q < O\) and is displaced away from the centre in the plane of the ring then it will continue moving till it hits the ring.
3 If \(q < O\) will perform SHM for small displacement along the axis.
4 All of the above.
PHXII01:ELECTRIC CHARGES AND FIELDS

358035 A ring of radius \(r\) carries a charge \(Q\) uniformly distributed over its length. A charge \(q\) is placed at its centre will experience a force equal to

1 \(\frac{{qQ}}{{8\pi {\varepsilon _0}{r^3}}}\)
2 \(\frac{{qQ}}{{4\pi {\varepsilon _0}{r^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358036 Charge \(q\) is uniformly distributed over a thin half ring of radius \(R\). The electric field at the centre of the ring is

1 \(\dfrac{q}{2 \pi^{2} \varepsilon_{0} R^{2}}\)
2 \(\dfrac{q}{4 \pi^{2} \varepsilon_{0} R^{2}}\)
3 \(\dfrac{q}{4 \pi \varepsilon_{0} R^{2}}\)
4 \(\dfrac{q}{2 \pi \varepsilon_{0} R^{2}}\)
AIIMS - 2008
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PHXII01:ELECTRIC CHARGES AND FIELDS

358032 A thin semi-circular ring of radius \(r\) has a positive charge \(q\) distributed uniformly over it. The net electric field \(\overrightarrow E \) at the centre \(O\) is
supporting img

1 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
2 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
3 \( - \frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
4 \( - \frac{q}{{4{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358033 A thin conducting ring of radius \(R\) is given a charge + \(Q\). The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E\). The electric field at the centre due to the charge on the part \(ACD\) of the ring is
supporting img

1 \(\sqrt 2 E\,\,{\rm{along}}\,\,OB\)
2 \(\sqrt 2 E\,\,{\rm{along}}\,\,KO\)
3 \(2E\,\,{\rm{along}}\,\,OK\)
4 \(\sqrt 3 E\,\,{\rm{along}}\,\,KO\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358034 A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring as shown in the figure. Then
supporting img

1 If \(q > O\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
2 If \(q < O\) and is displaced away from the centre in the plane of the ring then it will continue moving till it hits the ring.
3 If \(q < O\) will perform SHM for small displacement along the axis.
4 All of the above.
PHXII01:ELECTRIC CHARGES AND FIELDS

358035 A ring of radius \(r\) carries a charge \(Q\) uniformly distributed over its length. A charge \(q\) is placed at its centre will experience a force equal to

1 \(\frac{{qQ}}{{8\pi {\varepsilon _0}{r^3}}}\)
2 \(\frac{{qQ}}{{4\pi {\varepsilon _0}{r^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358036 Charge \(q\) is uniformly distributed over a thin half ring of radius \(R\). The electric field at the centre of the ring is

1 \(\dfrac{q}{2 \pi^{2} \varepsilon_{0} R^{2}}\)
2 \(\dfrac{q}{4 \pi^{2} \varepsilon_{0} R^{2}}\)
3 \(\dfrac{q}{4 \pi \varepsilon_{0} R^{2}}\)
4 \(\dfrac{q}{2 \pi \varepsilon_{0} R^{2}}\)
AIIMS - 2008
NEET DIGITAL LIBRARY
PHXII01:ELECTRIC CHARGES AND FIELDS

358032 A thin semi-circular ring of radius \(r\) has a positive charge \(q\) distributed uniformly over it. The net electric field \(\overrightarrow E \) at the centre \(O\) is
supporting img

1 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
2 \(\frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
3 \( - \frac{q}{{2{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
4 \( - \frac{q}{{4{\pi ^2}{\varepsilon _0}{r^2}}}\hat j\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358033 A thin conducting ring of radius \(R\) is given a charge + \(Q\). The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E\). The electric field at the centre due to the charge on the part \(ACD\) of the ring is
supporting img

1 \(\sqrt 2 E\,\,{\rm{along}}\,\,OB\)
2 \(\sqrt 2 E\,\,{\rm{along}}\,\,KO\)
3 \(2E\,\,{\rm{along}}\,\,OK\)
4 \(\sqrt 3 E\,\,{\rm{along}}\,\,KO\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358034 A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring as shown in the figure. Then
supporting img

1 If \(q > O\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre
2 If \(q < O\) and is displaced away from the centre in the plane of the ring then it will continue moving till it hits the ring.
3 If \(q < O\) will perform SHM for small displacement along the axis.
4 All of the above.
PHXII01:ELECTRIC CHARGES AND FIELDS

358035 A ring of radius \(r\) carries a charge \(Q\) uniformly distributed over its length. A charge \(q\) is placed at its centre will experience a force equal to

1 \(\frac{{qQ}}{{8\pi {\varepsilon _0}{r^3}}}\)
2 \(\frac{{qQ}}{{4\pi {\varepsilon _0}{r^2}}}\)
3 Zero
4 None of these
PHXII01:ELECTRIC CHARGES AND FIELDS

358036 Charge \(q\) is uniformly distributed over a thin half ring of radius \(R\). The electric field at the centre of the ring is

1 \(\dfrac{q}{2 \pi^{2} \varepsilon_{0} R^{2}}\)
2 \(\dfrac{q}{4 \pi^{2} \varepsilon_{0} R^{2}}\)
3 \(\dfrac{q}{4 \pi \varepsilon_{0} R^{2}}\)
4 \(\dfrac{q}{2 \pi \varepsilon_{0} R^{2}}\)
AIIMS - 2008