Electric Field
PHXII01:ELECTRIC CHARGES AND FIELDS

358188 Four point charges are placed at the corners of a square with diagonal 2\(a\) as shown. What is the total electric field at the center of the square?
supporting img

1 \(kq/{a^2}\) at an angle \({45^0}\) above the \( + x\)-axis
2 \(kq/{a^2}\) at an angle \({45^0}\) below the \( - x\)-axis
3 \(4kq/{a^2}\) at an angle \({45^0}\) above the \( - x\)-axis
4 \(4kq/{a^2}\) at an angle \({45^0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358189 Two particles \(A\) and \(B\) having equal charges are placed at a distance \(d\) apart. A third charged particle placed on the perpendicular bisect or of \(AB\) at distance \(x\). The third particle experiences maximum force when

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

358190 Four point charges \( + q, + q, - q\,{\rm{and}}\, - q\) are placed on the corners of a square of side length ‘\(a\)’ as shown in the figure. The magnitude of the electric field at a point which is at a distance \(x( > > a)\) from the centre along a line perpendicular to the plane of the square and passing through the centre is,
supporting img

1 \(\frac{{\sqrt 2 qa}}{{4\pi {\varepsilon _o}{x^3}}}\)
2 \(\frac{{q{\rm{a}}}}{{2\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
3 \(\frac{{\sqrt 2 qa}}{{2\pi {\varepsilon _o}{x^3}}}\)
4 \(\frac{{q{\rm{a}}}}{{4\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358191 Calculate \({E}\) at centre \((O)\) for the following figure.
supporting img

1 \({\dfrac{k Q}{25 a^{2}}}\)
2 \({\dfrac{4 k Q}{25 a^{2}}}\)
3 \({\dfrac{7 k Q}{5 a^{2}}}\)
4 \({\dfrac{3 k Q}{25 a^{2}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358192 Two charges of \(30\,\mu C\) and \( - 90\,\mu C\) are separated by a distance of \(24\,cm.\) Electrostatic field strength from the smaller charge is zero at a distance of

1 \(12\,cm\)
2 \(24\,cm\)
3 \(36\,cm\)
4 \(48\,cm\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358188 Four point charges are placed at the corners of a square with diagonal 2\(a\) as shown. What is the total electric field at the center of the square?
supporting img

1 \(kq/{a^2}\) at an angle \({45^0}\) above the \( + x\)-axis
2 \(kq/{a^2}\) at an angle \({45^0}\) below the \( - x\)-axis
3 \(4kq/{a^2}\) at an angle \({45^0}\) above the \( - x\)-axis
4 \(4kq/{a^2}\) at an angle \({45^0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358189 Two particles \(A\) and \(B\) having equal charges are placed at a distance \(d\) apart. A third charged particle placed on the perpendicular bisect or of \(AB\) at distance \(x\). The third particle experiences maximum force when

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

358190 Four point charges \( + q, + q, - q\,{\rm{and}}\, - q\) are placed on the corners of a square of side length ‘\(a\)’ as shown in the figure. The magnitude of the electric field at a point which is at a distance \(x( > > a)\) from the centre along a line perpendicular to the plane of the square and passing through the centre is,
supporting img

1 \(\frac{{\sqrt 2 qa}}{{4\pi {\varepsilon _o}{x^3}}}\)
2 \(\frac{{q{\rm{a}}}}{{2\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
3 \(\frac{{\sqrt 2 qa}}{{2\pi {\varepsilon _o}{x^3}}}\)
4 \(\frac{{q{\rm{a}}}}{{4\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358191 Calculate \({E}\) at centre \((O)\) for the following figure.
supporting img

1 \({\dfrac{k Q}{25 a^{2}}}\)
2 \({\dfrac{4 k Q}{25 a^{2}}}\)
3 \({\dfrac{7 k Q}{5 a^{2}}}\)
4 \({\dfrac{3 k Q}{25 a^{2}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358192 Two charges of \(30\,\mu C\) and \( - 90\,\mu C\) are separated by a distance of \(24\,cm.\) Electrostatic field strength from the smaller charge is zero at a distance of

1 \(12\,cm\)
2 \(24\,cm\)
3 \(36\,cm\)
4 \(48\,cm\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358188 Four point charges are placed at the corners of a square with diagonal 2\(a\) as shown. What is the total electric field at the center of the square?
supporting img

1 \(kq/{a^2}\) at an angle \({45^0}\) above the \( + x\)-axis
2 \(kq/{a^2}\) at an angle \({45^0}\) below the \( - x\)-axis
3 \(4kq/{a^2}\) at an angle \({45^0}\) above the \( - x\)-axis
4 \(4kq/{a^2}\) at an angle \({45^0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358189 Two particles \(A\) and \(B\) having equal charges are placed at a distance \(d\) apart. A third charged particle placed on the perpendicular bisect or of \(AB\) at distance \(x\). The third particle experiences maximum force when

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

358190 Four point charges \( + q, + q, - q\,{\rm{and}}\, - q\) are placed on the corners of a square of side length ‘\(a\)’ as shown in the figure. The magnitude of the electric field at a point which is at a distance \(x( > > a)\) from the centre along a line perpendicular to the plane of the square and passing through the centre is,
supporting img

1 \(\frac{{\sqrt 2 qa}}{{4\pi {\varepsilon _o}{x^3}}}\)
2 \(\frac{{q{\rm{a}}}}{{2\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
3 \(\frac{{\sqrt 2 qa}}{{2\pi {\varepsilon _o}{x^3}}}\)
4 \(\frac{{q{\rm{a}}}}{{4\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358191 Calculate \({E}\) at centre \((O)\) for the following figure.
supporting img

1 \({\dfrac{k Q}{25 a^{2}}}\)
2 \({\dfrac{4 k Q}{25 a^{2}}}\)
3 \({\dfrac{7 k Q}{5 a^{2}}}\)
4 \({\dfrac{3 k Q}{25 a^{2}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358192 Two charges of \(30\,\mu C\) and \( - 90\,\mu C\) are separated by a distance of \(24\,cm.\) Electrostatic field strength from the smaller charge is zero at a distance of

1 \(12\,cm\)
2 \(24\,cm\)
3 \(36\,cm\)
4 \(48\,cm\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358188 Four point charges are placed at the corners of a square with diagonal 2\(a\) as shown. What is the total electric field at the center of the square?
supporting img

1 \(kq/{a^2}\) at an angle \({45^0}\) above the \( + x\)-axis
2 \(kq/{a^2}\) at an angle \({45^0}\) below the \( - x\)-axis
3 \(4kq/{a^2}\) at an angle \({45^0}\) above the \( - x\)-axis
4 \(4kq/{a^2}\) at an angle \({45^0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358189 Two particles \(A\) and \(B\) having equal charges are placed at a distance \(d\) apart. A third charged particle placed on the perpendicular bisect or of \(AB\) at distance \(x\). The third particle experiences maximum force when

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

358190 Four point charges \( + q, + q, - q\,{\rm{and}}\, - q\) are placed on the corners of a square of side length ‘\(a\)’ as shown in the figure. The magnitude of the electric field at a point which is at a distance \(x( > > a)\) from the centre along a line perpendicular to the plane of the square and passing through the centre is,
supporting img

1 \(\frac{{\sqrt 2 qa}}{{4\pi {\varepsilon _o}{x^3}}}\)
2 \(\frac{{q{\rm{a}}}}{{2\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
3 \(\frac{{\sqrt 2 qa}}{{2\pi {\varepsilon _o}{x^3}}}\)
4 \(\frac{{q{\rm{a}}}}{{4\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358191 Calculate \({E}\) at centre \((O)\) for the following figure.
supporting img

1 \({\dfrac{k Q}{25 a^{2}}}\)
2 \({\dfrac{4 k Q}{25 a^{2}}}\)
3 \({\dfrac{7 k Q}{5 a^{2}}}\)
4 \({\dfrac{3 k Q}{25 a^{2}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358192 Two charges of \(30\,\mu C\) and \( - 90\,\mu C\) are separated by a distance of \(24\,cm.\) Electrostatic field strength from the smaller charge is zero at a distance of

1 \(12\,cm\)
2 \(24\,cm\)
3 \(36\,cm\)
4 \(48\,cm\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358188 Four point charges are placed at the corners of a square with diagonal 2\(a\) as shown. What is the total electric field at the center of the square?
supporting img

1 \(kq/{a^2}\) at an angle \({45^0}\) above the \( + x\)-axis
2 \(kq/{a^2}\) at an angle \({45^0}\) below the \( - x\)-axis
3 \(4kq/{a^2}\) at an angle \({45^0}\) above the \( - x\)-axis
4 \(4kq/{a^2}\) at an angle \({45^0}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358189 Two particles \(A\) and \(B\) having equal charges are placed at a distance \(d\) apart. A third charged particle placed on the perpendicular bisect or of \(AB\) at distance \(x\). The third particle experiences maximum force when

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

358190 Four point charges \( + q, + q, - q\,{\rm{and}}\, - q\) are placed on the corners of a square of side length ‘\(a\)’ as shown in the figure. The magnitude of the electric field at a point which is at a distance \(x( > > a)\) from the centre along a line perpendicular to the plane of the square and passing through the centre is,
supporting img

1 \(\frac{{\sqrt 2 qa}}{{4\pi {\varepsilon _o}{x^3}}}\)
2 \(\frac{{q{\rm{a}}}}{{2\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
3 \(\frac{{\sqrt 2 qa}}{{2\pi {\varepsilon _o}{x^3}}}\)
4 \(\frac{{q{\rm{a}}}}{{4\pi {\varepsilon _o}{{\rm{x}}^3}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358191 Calculate \({E}\) at centre \((O)\) for the following figure.
supporting img

1 \({\dfrac{k Q}{25 a^{2}}}\)
2 \({\dfrac{4 k Q}{25 a^{2}}}\)
3 \({\dfrac{7 k Q}{5 a^{2}}}\)
4 \({\dfrac{3 k Q}{25 a^{2}}}\)
PHXII01:ELECTRIC CHARGES AND FIELDS

358192 Two charges of \(30\,\mu C\) and \( - 90\,\mu C\) are separated by a distance of \(24\,cm.\) Electrostatic field strength from the smaller charge is zero at a distance of

1 \(12\,cm\)
2 \(24\,cm\)
3 \(36\,cm\)
4 \(48\,cm\)