Equipotential surface through a point is normal to the electric field in any charge arrangement. This claim will be supported by contradiction. Assuming the assumption is false, an electric field component can exist along the equipotential surface. A test charge is now moved along the equipotential surface given by dW=qEdx, and non-zero work is done on it. However, no work is done on the test charge when it moves through an equipotential surface. As a result, the assumption was incorrect. As a result, no component of the electric field can be found along the equipotential surface, implying that it must be perpendicular to it.
Part 1: For spherical metal bobs The Earth's magnetic field was also experienced by metallic bob due to its conducting nature. When metallic bob falls freely from a height, the current is created by the metallic bob as it falls through the Earth's magnetic field. So, according to Lenz's law, the induced current opposes the metallic bob's free-falling motion and causes an upward push, which slows down the speed of the metallic bob to some extent. Part 2: For the spherical glass bob Glass bob, on the other hand, does not experience any of these forces due to its non-conducting nature, and hence only senses Earth gravitational attraction. As a result, glass bob will arrive at the Earth before the sun.
Object distance, according to the query, is 20 cm. Also, the image distance is 20 cm. The rays refracted first by the lens and then by the flat mirror must be retracing their course because the object's image I corresponds with O. Only when rays refracted by the convex lens fall naturally on the mirror, forming a beam parallel to the lens's primary axis, is this condition achieved. As a result, the object O must be at the convex lens's focus. CO = 20 cm = f
The Lorentz magnetic force is calculated using the following formula: F (vector) = q ( V (vector) × B(vector) ) The magnitude of the moving charge is denoted by q. The magnetic force is parallel to the plane containing the velocity vector V and the magnetic field vector B.
The relative permeability of a paramagnetic material is between 1< 𝜇ᵣ < 1+𝜀, while its susceptibility is between 0<X<𝜀. As a result, 'A' is a para-magnetic substance with a positive susceptibility. Because its relative permeability is somewhat larger than unity, this is the case. The relative permeability of a diamagnetic substance is between 0 < 𝜇ᵣ < 1 and its susceptibility is between -1 < X<0. As a result, 'B' is a diamagnetic substance with a negative susceptibility. This is due to the fact that its relative permeability is less than one. The relative permeability and susceptibility are denoted by 𝜇ᵣ and x.
Here, E (vector) = 5 x 10³ i^ N/C, i.e., field is along positive direction of X - axis. Surface area, A = 10 cm x 10 cm = 0.10 m x 0.10 m = 10⁻²m² (i) When plane is parallel to Y-Z plane, the normal to plane is along X - axis. Here θ = 0° ϕ = EA cosθ = 5x 10³ x 10² cos0° = 50 NC¹ m²
(ii) When the plane makes a 30° angle with the X-axis, the normal to its plane makes 60° angle with X - axis. Hence θ = 60° ϕ = EA cosθ = 5x 10³ x 10² cos60° 25 NC¹ m²
