# Electric Field Due to an Arc at the Centre

## Trending Questions

**Q.**

A rod of length L has a total charge Q distributed uniformly along its length. It is bent in th shape of a semicircle. Find the magnitude of the electric field at the centre of curvatere of he semicircle.

**Q.**Figure shows a rod AB, which is bent in a 120∘ circular arc of radius R. A charge (−Q) is uniformly distributed over rod AB. What is the electric field →E at the centre of curvature O ?

- 3√3Q16π2ε0R2(ˆi)
- 3√3Q8π2ε0R2(ˆi)
- 3√3Q8πε0R2(ˆi)
- 3√3Q8π2ε0R2(−ˆi)

**Q.**The linear charge density of a uniform semicircular wire varies with θ as shown in the figure as λ=λ0cosθ. Find the charge on the wire if R is the radius of the ring.

- 3λ0R
- λ0R
- 2λ0R3
- 2λ0R

**Q.**For the given charge distribution on the ring, the net electric field at the centre of non-conducting ring is

(Assume the part of ring in first and third quadrant is neutral, second quadrant is positively charged, fourth quadrant is negatively charged)

- 180√2 N/C
- 180√3 N/C
- 180√5 N/C
- 180√7 N/C

**Q.**

If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be

**Q.**A thin Non-conducting rod is bent into a semicircle of radius r. A charge +Q is uniformly distributed along the upper half and a charge −Q is uniformly distributed along the lower half, as shown in figure. Find the electric field E at P.

- Qπ2ϵ0r2
- 2Qπ2ϵ0r2
- 4Qπ2ϵ0r2
- Q4π2ϵ0r2

**Q.**A 10 cm long rod carries a charge of +50μC distributed uniformly along its length. Find the magnitude of the electric field at a point 10 cm from both the ends of the rod.

- 4.2×107 N/C
- 5.2×107 N/C
- 6.2×107 N/C
- 7.2×107 N/C

**Q.**To get the formula of electric field due to a ring at the centre from the formula of electric field due to an arc at centre, replace θ with

- 90∘
- 180∘
- 45∘
- 360∘

**Q.**

A magnetic wire of dipole moment $4\mathrm{\xcf\u20ac}{\mathrm{Am}}^{2}$ is bent in the form of a semi-circle. What is the new magnetic moment is?

${\mathrm{\xcf\u20acAm}}^{2}$

$2{\mathrm{\xcf\u20acAm}}^{2}$

$8A{m}^{2}$

$4{\mathrm{\xcf\u20acAm}}^{2}$

**Q.**A thin glass rod is bent into a semicircle of radius r. A charge +Q is uniformly distributed along the upper half and a charge –Q is uniformly distributed along the lower half, as shown in the figure. The electric field E at, P (the centre of the semicircle, is)

- Qπ2ε0r2
- 2Qπ2ε0r2
- 4Qπ2ε0r2
- Q4π2ε0r2

**Q.**A charge q is uniformly distributed on a spherical shell of radius R. The electric field at a distance 4R3 from the centre will be

- 9q64πε0R2
- q4πε0R3
- 3q16πε0R2
- Zero

**Q.**If O is the center of a ring of radius r, then find the potential at point O due to half ring that has a linear charge density λ.

- λ4ϵ0
- λ4π2ϵ0r
- λ4πϵ0r
- λ4πϵ0r2

**Q.**The linear charge density on a ring which varies with angle θ can be represented as λ=Kcosθ2, wherek = 2 cm^{-1}and\theta$ is the angle subtended by the radius of the ring with the horizontal. The potential at the centre of the ring is

**Q.**Charge q is uniformly distributed over a thin half ring of radius R. The electric field at the centre of the ring is

- q2π2ϵ0R2
- q4π2ϵ0R2
- q4πϵ0R2
- q2πϵ0R2

**Q.**For the given semi-infinite rod of uniformly distributed line charge, angle (θ) between net electric field and component of net electric field perpendicular to the axis of line charge at the point P is

- 30∘
- 45∘
- 60∘
- 15∘

**Q.**A large plane charged sheet having surface charge density σ=+2×10−6 C/m2 lies in the x-y plane. Find the flux of the electric field through a circular area of radius 1 cm lying completely in the region where x, y, z all are positive and with its normal making an angle of 60∘ with the z-axis.

- 16.3 Nm2/C
- 17.3 Nm2/C
- 8.15 Nm2/C
- 34.6 Nm2/C

**Q.**For the given uniformly charged ring sector symmetrically placed about Y axis, net electric filed at the point P along X-direction is

[l is the length of the arc, λ is linear charge density, R is radius of sector]

- 2kλRsin(l2R)
- 2kλRsin(lR)
- 2kλR
- Zero

**Q.**For the given charge distribution, the net electric field at the centre of the non-conducting ring is

- 180 N/C
- 220 N/C
- 320 N/C
- 360 N/C

**Q.**For the given uniformly charged ring of linear charge density +10 nC/m, the electric field in y− direction at point P is

- 100 N/C
- 200 N/C
- Zero
- 150 N/C

**Q.**Two mutually perpendicular infinite wires carry positive charge densities λ1 and λ2. The electric lines of force makes angle α with second wire then λ1λ2 is

- tan2α
- cot2α
- sin2α
- cos2α

**Q.**An insulating rod of length l carries a charge q uniformly distributed on it. The rod is pivoted at one of its ends, and it is rotated at a frequency f about a fixed perpendicular axis in the horizontal plane. The magnetic moment of the rod is

- πqfl212

- πqfl22

- πqfl26

- πqfl23

**Q.**A 10 cm long rod carries a charge of +50μC distributed uniformly along its length. Find the magnitude of the electric field at a point 10 cm from both the ends of the rod.

- 4.2×107 N/C
- 5.2×107 N/C
- 6.2×107 N/C
- 7.2×107 N/C

**Q.**

A circular arc has a radius of 0.1m. The angle it subtends at the Centreis π6 . If the charge it carries is 10C. what is the linear charge density of the wire?

192.3 c/m

215.2 c/m

50 c/m

500 c/m

**Q.**A large charged conducting sheet is placed in a uniform electric field, perpendicularly to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet is E1=5×105 V/m and on the right it is E2=3×105 V/m. The sheet experiences a net electric force of 0.08 N. Find the area of one face of the sheet.( Assume the external field to remain constant after introducing the large sheet)

[k=14πε0=9×109 Nm2C−2]

- 3.6π×10−2 m2
- 0.9π×10−2 m2
- 1.8π×10−2 m2
- None

**Q.**Find the magnitude of the electric field (|−−→Eind|) at the center of the sphere due to the induced charges on the sphere.

- Kq2
- Kq8
- Kq5
- Kq4

**Q.**Charge Q is distributed uniformly on length l of a wire. It is bent in the form of a semicircular ring. Find the electric field at the centre of the ring.

- Q2πε0l2
- Q4πε0l2
- Qπ4ε0l2
- Q2ε0l2

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

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

**Q.**For the given charge distribution on the ring, the net electric field at the centre of non-conducting ring is

(Assume the part of ring in first and third quadrant is neutral, second quadrant is positively charged, fourth quadrant is negatively charged)

- 180√2 N/C
- 180√3 N/C
- 180√5 N/C
- 180√7 N/C

**Q.**A long straight conductor, carrying a current i, is bent to form an almost complete circular loop of radius r as shown. The magnetic field at the centre of the loop :

- has magnitude μ0ir(1−1π)
- has magnitude μ0ir(1+1π)
- has magnitude μ0i2r(1−1π)
- has magnitude μ0i2r(1+1π)

**Q.**A thin glass rod is bent into a semicircular shape of radius R. A charge +Q is uniformly distributed along the upper half and a charge −Q is distributed uniformly along the lower half as shown. The electric field at the centre P is:

- √2Q4πε0R2
- Q√2πε0R2
- Q2πε0R2
- Qπ2ε0R2