# Electric Field Due to a Ring Along the Axis

## Trending Questions

**Q.**Find the electric field at point P as shown in the figure on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a=√32L.

- Q4πϵ0L2
- Q3πϵ0L2
- √3Q4πϵ0L2
- Q2√3πϵ0L2

**Q.**What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is l and perpendicular to each other ?

- 14πϵ0ql2
- 14πϵ0q(2l2)(2√2−1)
- q4πϵ0(2l)2
- 14πϵ02q2l2(√2)

**Q.**Four charges +q, +q, −q and −q are placed respectively at the corners A, B, C and D of a square of side a arranged in the given order. E and F are midpoints of side BC and CD respectively. O is the center of the square.

(i) The electric field at O is

[1 Mark]

- q√2πε0a2
- q√3πε0a2
- √3qπε0a2
- √2qπε0a2

**Q.**Two charges 4q and q are placed 30 cm apart. At what point, the value of electric field will be zero?

- 10 cm away from q and between the charges.
- 20 cm away from q and between the charges.
- 15 cm away from q and between the charges.
- 25 cm away from q and between the charges.

**Q.**A cube of side l has point charges (+q) at each of its vertices except at the origin where the charge is (−q) as shown in the figure. The electric field at the centre of the cube is

- q3√3πϵ0l2(^x+^y+^z)
- 2q3√3πϵ0l2(^x+^y+^z)
- −q3√3πϵ0l2(^x+^y+^z)
- −2q3√3πϵ0l2(^x+^y+^z)

**Q.**A ring of radius R is charged uniformly with a charge +Q . The electric field at any point on its axis at a distance r from the circumference of the ring will be

- KQr
- KQrR3
- KQr2
- KQr3(r2−R2)12

**Q.**Four positive charges (2√2−1)Q are arranged at the four corners of a square. Another charge q is placed at the centre of the square. Resulting field acting on each corner will be zero if q is

- −7Q4
- −4Q7
- −Q
- −(√2+1)Q

**Q.**

Electric field vs. distance along the axis is shown for a uniformly charged circular ring

Which of the following represents the complete graph?

**Q.**Two point charges (+ Q) and (-2 Q) are fixed on the X-axis at positions a and 2a from origin respectively. At what positions on the axis, the resultant electric field is zero

- Only x=√2a
- Only x=−√2a
- x=3a2 only
- Both x=±√2a

**Q.**Two charges q1 and q2 are kept on x− axis and electric field at different points on x− axis is plotted against x. Choose correct statement about nature and magnitude of q1 and q2.

- q1+ve, q2−ve; |q1|>|q2|
- q1+ve, q2−ve; |q1|<|q2|
- q1−ve, q2+ve; |q1|>|q2|
- q1−ve, q2+ve; |q1|<|q2|

**Q.**Three charged particles A, B and C with charges −4q, 2q and −2q are present on the circumference of a circle of radius d. The charged particle A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x− direction is:

- √3qπϵ0d2
- 2√3qπϵ0d2
- √3q4πϵ0d2
- 3√3q4πϵ0d2

**Q.**

Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.

**Q.**A charge 10−9 C is located at the origin of a coordinate system and another charge Q at (2, 0, 0). If the x− component of the electric field at (3, 1, 1) is zero, calculate the value of Q.

- 4.3×10−10 C
- 2.3×10−10 C
- −4.3×10−10 C
- −2.3×10−10 C

**Q.**For the two fixed infinite line charges, the net electric field is zero at a point P between them. The distance of the point P from the left infinite line charge is

- 0.25 m
- 1.25 m
- 2.25 m
- 3.25 m

**Q.**Five point charges (+q each) are placed at the five vertices of a regular hexagon of side 2a. What is the magnitude of the net electric field at the centre of the hexagon?

- 14πϵ0qa2
- q16πϵ0a2
- √2q4πϵ0a2
- 5q16πϵ0q2

**Q.**

The distance of point P on the axis from the Centre of a uniformly charged circular ring where the electric field is maximum, is 2−nR(given radius of the ring is R). The value of n in decimal form is

**Q.**A charge q is placed in the middle of a line joining the two equal and like point charges Q. This system will remain in equilibrum for which the value of q is-

- −Q3
- −Q4
- Q2
- −Q2

**Q.**An infinite number of identical charges, each +q coulomb, are placed along x-axis at x=1 m, 3 m, 9 m, ... Calculate the electric field at the point x=0 due to these charges.

- 14πε09q8 NC−1
- 14πε09q10 NC−1
- 14πε09q7 NC−1
- 14πε09q5 NC−1

**Q.**Two concentric rings, one of radius ‘a’ and the other of radius ‘b’, have the charges +q, and −(25)−32 respectively, as shown in the figure. Find the ratio ba if a charge particle placed on the axis at z = a is in equilibrium.

**Q.**

P is a point on the axis of a ring with Centre O and radius 0.1m. The ring is uniformly charged with linear charge density 0.5 c/m. Given OP = 0.1 m, the electric field at P is approximately ten to the power

**Q.**ABC is a right-angle triangle with right angle A and AB=AC=30 cm if the charge on B and C is 4×10−3 μC then the electric field at A will be

- 400 N/C parallel to BC
- 800 N/C parallel to BC
- 400√2 N/C perpendicular to BC
- 800 N/C perpendicular to BC

**Q.**The magnitude of electric field E in the annular region of a charged cylindrical capacitor

- varies as 1r, where r is the distance from the axis.
- varies as 1r2, where r is the distance from the axis.
- is the same throughout.
- is higher near the outer cylinder than near to it.

**Q.**

Uniformly charged ring is shown is figure, E due to ring is maximum at

- Centre
- ∞
- R distance from centre
- R√2 distance from centre

**Q.**Charges −q and +q located at A and B respectively and OP is perpendicular to line AB. A charge Q is placed at P, where OP=y (y>>2a). The charge Q experiences an electrostatics force F. If Q is now moved along the equatorial line to P′ such that OP′=y3, the force experienced by charge Q will be close to

(Assume y2>>2a)

- F/3
- F/27
- 9F
- 27F

**Q.**Consider two point charges, q3 and −2q3 at point B and C respectively as shown in the figure. Take O to be the centre of the circle of radius R and ∠CAB=60∘. The magnitude of force between the charges is

- q254πϵ0R2
- q227πϵ0R2
- q225πϵ0R2
- q260πϵ0R2

**Q.**A conducting sphere of radius R having charge q is joined to another conducting sphere of radius 2R having charge −2q. The charge flowing between them will be

- q
- 2q3
- q3
- 4q3

**Q.**For the given uniformly charged ring, which of the following curve of electric field (E) versus distance from the centre of ring (x) along x− axis is correct?

[Consider only right side of ring]

**Q.**Which of the following graphs correctly represent the variation of electric field E vs r for a ring, where r represents the distance from the centre of ring along its axis.

**Q.**

Positive charge Q is distributed uniformly over a ircular ring of radius R. A particle having having a mass ma and a negative charge q, is placed on its axis at a distanc ex from the centre. Find the force on the particle. Assuming x<< R, Find the time period of oscillation of the particle if it is released from there.

**Q.**

P is a point on the axis of a ring with Centre 0 and radius 0.1m. The ring is uniformly charged with linear charge density 0.5 c/m. Given OP = 0.1 m, the electric field at P is approximately ten to the power ____ in SI units.