Two small spheres each of mass are suspended from a point by threads long. They are equally charged and repel each other to a distance of . Then charge on each of the sphere is . The value of ‘a’ will be ________. [Take ]
Step 1: Given
Mass of each sphere:
Length of threads:
Distance between masses:
Charge on each sphere:
Acceleration due to gravity:
Step 2: Formula Used
Step 3: Find an expression for
Find the value of which will be equal to the weight of the mass (acting downwards) in order to balance it.
Find the value of which will be equal to the electrostatic force acting on the charge in order to balance it.
Find an expression for by dividing equation 2 by equation 1
Find an expression for using trigonometry
Step 4: Find the value of a
Find the value of charge by equating both the values of tangent of angle, that is, equate equation 3 and equation 4.
Substitute the value of charge obtained in .
Hence, Two small spheres each of mass are suspended from a point by threads long. They are equally charged and repel each other to a distance of . Then charge on each of the sphere is . The value of ‘a’ will be