Physics · Electric field: electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in a uniform electric field
A thick shell with inner radius and outer radius has a uniform charge density It
A thick shell with inner radius \( R \) and outer radius \( 3 R \) has a uniform charge density \( \sigma c / m^{3} . \) It has a spherical cavity of radius \( R \) as shown in the figure. the electric field at the centre of the cavity is
- A. zero
- B. \( 2 \sigma R / \varepsilon_{0} \)
- C. \( 3 \sigma R / 4 \varepsilon_{0} \)
- D. \( 7 \sigma R / 12 \varepsilon_{0} \)
Step-by-step solution
The electric field at the center of the spherical cavity is found using superposition: consider a uniformly charged sphere of radius 3R (density σ), subtract a sphere of radius R at the center (to create the inner hollow), and subtract another sphere of radius R at the cavity's center (to create the cavity). The field at the cavity's center is due to the sphere of radius 3R and the negative sphere at the center. The cavity's own field is zero. With the cavity center at distance 2R from the common center, the field from the sphere of radius 3R is E1 = (σ*(2R))/(3ε0) outward, and from the negative sphere at the center is E2 = -(σ R^3)/(3ε0*(2R)^2) inward. Adding gives E = (2σR)/(3ε0) - (σR)/(12ε0) = (8σR - σR)/(12ε0) = (7σR)/(12ε0).
Related MCQs
- An electric dipole is placed in a non- uniform electric field, then…
- A red LED emits light at uniformly around it. The amplitude of the electric filed of the light at a distance of form the diode is:…
- An electric dipole placed with its axis in the direction of a uniform electric field experiences:…
- A free electron in an electric field…
- A point charge is brought in an electric field. The electric field at a nearby point: This question has multiple correct options…