(8%) Problem 11: A 4.8 g charged insulating ball hangs on a 1.25 cm long string

Question

(8%) Problem 11: A 4.8 g charged insulating ball hangs on a 1.25 cm long string in a uniform horizontal electric field as shown in the fi gure Otheexpertta.com - Given the charge on the ball is 29 C , find the strength of the field in NC. Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: S (5% per attempt) detailed view cosO cotan0 asin) acos0 atan)acotan) sinhO cosh tanh cotanh0 Degrees O Radians sinO HOME 0 END DELCLEAR Submit Hint I give up! Hints: 1 % deduction per hint. Hints remaining: 1 Feedback: 1% deduction per feedback.

Explanation / Answer

here,

mass , m = 4.8 g = 0.0048 kg

length , l = 1.25 cm = 0.0125 m

charge , q = 29 uC= 29 * 10^-6 C

theta = 8 degree

let the tension in the string be T and electric feild be E

equating the forces vertically

T * cos(theta) = m * g

T * cos(8) = 0.004.8 * 9.81 . ...(1)

and

equating the forces horizontally

T * sin(theta) = q * E

T * sin(8) = 29 * 10^-6 * E ...(2)

from (1) and (2)

tan(8) = 29 * 10^-6 * E /(0.004.8 * 9.81 )

solving for E

E = 228.2 N/C

the magnitude of electric feild is 228.2 N/C

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